Answer:
A. 19 years old
Step-by-step explanation:
A person at the age of 19 is probably still in college . He/She is probably investing more time and finance in his/her education. A person at age 19 is still building his or her career . He/she is likely to have limited working experience. He/she has more years ahead of him to invest his little income(that is if he has any) for a longer term plan like owning a house and building a business.
In fact at age 19 a person is more concern in his/her career development and studies. Buying a house is most likely a long time goal for a person of 19 years old because he has so many year ahead of him to gather or create wealth for himself.
The other ages 59, 79 and 69 years are individuals who have probably amassed wealth . They probably have over 3 decades of working experience and this working years will reflect in their savings. people at this age have shorter time to work or are probably even retired.
Answer:
A. 19 years old
Step-by-step explanation:
19 years old because usually by the time someone between the ages of 59 and 79 should already own or be renting a house if they have set their financial goals correctly.
Suppose P(x) represents the profit on the sale of x Blu-ray discs. If P(1,000) = 5,000 and P'(1,000) = −3, what do these values tell you about the profit? P(1,000) represents the profit on the sale of Blu-ray discs. P(1,000) = 5,000, so the profit on the sale of Blu-ray discs is $ . P'(x) represents the as a function of x. P'(1,000) = −3, so the profit is decreasing at the rate of $ per additional Blu-ray disc sold.
Answer:
Step-by-step explanation:
We are told that P(x) is the profit of saling x blu ray discs. P(1000) is our profit for selling 1000 blu ray discs. So, our profit is 5000. Recall that the derivative P'(x) represents the rate at which the function P(x) is increasing/decreasing (increasing if P'(x) is positive, or decreasing otherwise) by increasing the values of x. In this case P'(1000)=-3, so the profit will decrease -3 if we increase x in one unit.
If eggs cost $3 per dozen, how much would 8 eggs cost?
Answer:
$2
Step-by-step explanation:
Because 3/12 is 0.25 and then you multiply it by 8 to get 2.
A scientist studying water quality measures the lead level in parts per billion (ppb) at each of 49 randomly chosen locations along a water line. Suppose that the lead levels across all the locations on this line are strongly skewed to the right with a mean of 17 ppb and a standard deviation of 14 ppb. Assume that the measurements in the sample are independent. What is the probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb? Choose 1 answer: A) Plæ <15) = 0.02 B) Plū<15) – 0.16 C) Plē <15) 0.30 D) Plö < 15) – 0.44 E) We cannot calculate this probability because the sampling distribution is not normal.
Complete Question
The complete qustion is shown on the first uploaded image
Answer:
The correct option is B
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 49[/tex]
The mean is [tex]\mu = 17ppb[/tex]
The standard deviation is [tex]\sigma = 14 ppb[/tex]
Generally the standard error of this measurement is mathematically represented as
[tex]\sigma_z = \frac{\sigma}{\sqrt{n} }[/tex]
substituting values
[tex]\sigma_{\= x} = \frac{14}{\sqrt{49} }[/tex]
[tex]\sigma_{\= x} = 2[/tex]ppb
Now the probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb represented as P(X < 15 )
Next is to find the z value
[tex]z = \frac{\mu -\sigma }{\sigma_{\= x}}[/tex]
[tex]z = \frac{15-17}{2}[/tex]
[tex]z = -1[/tex]
Now checking the z-table for the z-score of -1 we have
[tex]P(X<15) = P(Z < -1 )= 0.16[/tex]
Using the normal distribution and the central limit theorem, it is found that there is a 0.16 = 16% probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb, hence option B is correct.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X. By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex], considering a sample size of at least 30 for a skewed variable.In this problem:
Mean of 17 ppb, hence [tex]\mu = 17[/tex].Standard deviation of 14 ppb, hence [tex]\sigma = 14[/tex].Sample of 49, hence [tex]n = 49, s = \frac{14}{\sqrt{49}} = 2[/tex]The probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb is the p-value of Z when X = 15, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{15 - 17}{2}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a p-value of 0.16
0.16 = 16% probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb, hence option B is correct.
For more on the normal distribution and the central limit theorem, you can check https://brainly.com/question/24663213
A box contains five keys, only one of which will open a lock. Keys are randomly selected and tried, one at a time, until the lock is opened (keys that do not work are discarded before another is tried). Let Y be the number of the trial on which the lock is opened. Find the probability function for Y.
The "density of probability" is represented by the Y-axis in the normal distribution.It indicates the likelihood of finding values close to comparable places on the X-axis.
Find the probability f ?Y is the number of trial on which lock is opend so, P(Y=y) be the probability that key opens the lock on y th trial Lets draw first key
p(1 st key opens the lock) =1-1/5= 4/5
Hence p(1 st key does not open the lock = 1- 1/5 =4/5
Since p (Lock is opened on 1 st triual ) = p(1st key opens the lock )
Hence , P(Y =2 ) 1/4 .4/5 = 1/5
p( y = 4) = 1/5
p(y = 5 ) =1/5
To learn more about probability function refer
https://brainly.com/question/28021875
#SPJ2
00:00
Muriel has been a member of the Solaris Gym for 372 days,
Ben has been a member for 1 year, 2 weeks, 3 days.
Part A
Who has been a member of the Solaris Gym longer?
Use the drop-down menus to show and explain your answer.
Choose...
has been a member longer because 1 year, 2 weeks, 3 days is
Choose...
than 372 days
00:00
Part B
How much longer? Assume that it is not a leap year. Enter your answer in the box.
days
Answer:
A: Ben has been a member longer because 1 year, 2 weeks, 3 days is longer than 372 days.
B: 10 days longer
Step-by-step explanation:
1 year, 2 weeks, 3 days is 382 days -> 365 + 14 + 3 = 382
Mr Smith had four daughters.Each daughter has four brothers.How many children does Mr Smith have
Starting off, you already know he has 4 daughters and for every daughter there are 4 sons.
So, we take the 4 daughters and add 4 to each one:
1 daughter + 4 sons = 5 children
We complete that equation 4 times for each daughter, and we end up with 20 children as our answer.
Hope this helps you out a bit! Stay safe and stay healthy! :D
According to Net Market Share, Microsoft's Internet Explorer browser has 53.4% of the global market. A random sample of 70 users was selected. What is the probability that 32 or more from this sample used Internet Explorer as their browser?
Answer:
Probability that 32 or more from this sample used Internet Explorer as their browser is 0.9015.
Step-by-step explanation:
We are given that according to Net Market Share, Microsoft's Internet Explorer browser has 53.4% of the global market.
A random sample of 70 users was selected.
Let [tex]\hat p[/tex] = sample proportion of users who used Internet Explorer as their browser.
The z score probability distribution for sample proportion is given by;
Z = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, p = population proportion of users who use internet explorer = 53.4%
[tex]\hat p[/tex] = sample proportion = [tex]\frac{32}{70}[/tex] = 0.457
n = sample of users = 70
Now, probability that 32 or more from this sample used Internet Explorer as their browser is given by = P( [tex]\hat p[/tex] [tex]\geq[/tex] 0.457)
P( [tex]\hat p[/tex] [tex]\geq[/tex] 0.457) = P( [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] [tex]\geq[/tex] [tex]\frac{0.457-0.534}{\sqrt{\frac{0.457(1-0.457)}{70} } }[/tex] ) = P(Z [tex]\geq[/tex] -1.29)
= P(Z [tex]\leq[/tex] 1.29) = 0.9015
The above probability is calculated by looking at the value of x = 1.29 in the z table which has an area of 0.9015.
Cuanta cartulina se necesita para construir un prisma rectangular para cuya base mide 10cm y tiene 6cm de altura
Answer:
i dont understand the language
Step-by-step explanation:
PLEASE ANSWER I NEED THIS NOW The blue dot is at what value on the number line?
Answer:
-10
Step-by-step explanation:
goes up by 4 each value
Answer:
-10
Step-by-step explanation:
in that chain,
it is 10,6,2,-2,-6,-10
Reduce the fraction to lowest terms. Do not use spaces in your answer.
Answer:
-2x/yz
Step-by-step explanation:
You can cancel out terms using division and properties of exponents. x^a/x^b = x^a-b
300 students in a high school freshman class are surveyed about what kinds of pets they have. Of the 300
students, 200 have a dog, 180 have a cat, and 150 have a cat and a dog. Using this information, answer
• each of the following questions.
Let D be the event that a randomly selected student has a dog and C be the event that a randomly
selected student has a cat.
What is P(D), the probability that a student in the class has a dog?
What is P(C), the probability that a student in the class has a cat?
What is P(D and C), the probability that a student in the class has a dog and a cat?
What is P(D or C), the probability that a student in the class has a dog or a cat?
Answer:
Step-by-step explanation:
What is P(D), the probability that a student in the class has a dog?
D=66%
What is P(C), the probability that a student in the class has a cat?
C=60%
What is P(D and C), the probability that a student in the class has a dog and a cat?
DC=50%
A 6) Set both given equations equal to zero, then combine them into one standard form
equation. Simplify if possible.
7x + 3 = 5 and y-1 = 6
The equation in standard form is given by:
[tex]7x + y - 9 = 0[/tex]
------------------
The general equation in standard form is:
[tex]Ax + By + C = 0[/tex]
------------------
The first equation is:
[tex]7x + 3 = 5[/tex]
Setting equal to zero:
[tex]7x + 3 - 5 = 0[/tex]
[tex]7x - 2 = 0[/tex]
------------------
The second equation is:
[tex]y - 1 = 6[/tex]
[tex]y - 1 - 6 = 0[/tex]
[tex]y - 7 = 0[/tex]
------------------
Combining them, and placing in standard form:
[tex]7x - 2 + y - 7 = 0 + 0[/tex]
[tex]7x + y - 9 = 0[/tex]
A similar problem is given at https://brainly.com/question/14664782
Please answer this correctly
Answer:
54 9/10
Step-by-step explanation:
The perimeter is the sum of all the sides
13 1/4 + 12 1/5 + 18 1/4 + 11 1/5
Add up the whole numbers
13+12+18+11 = 54
1/4+1/5+1/4+1/5
2/4+2/5
1/2+2/5
Get a common denominator
1/2*5/5 + 2/5*2/2
5/10 + 4/10
9/10
Add them back together
54 9/10
The red function was transformed into the blue function. Which transformations have occurred?
Answer:
Translated 3 units down 2 units left.
Step-by-step explanation:
It looks like the functions are the same, so if you see, it was translated 3 units down and 2 units left.
A manufacturer uses 34 yard of fabric in each skirt.
How many yards of fabric will the manufacturer use in 4 skirts? in 7 skirts? in 9 skirts?
Answer:
She would use 136 yards in 4 skirts, 238 yards in 7 skirts, and 306 yards in 9 skirts. Hope this helps
Step-by-step explanation:
II. The results of a recent survey indicate that the average new car costs $23,000, with a standard deviation of $3,500. The price of cars is normally distributed. a. What is a Z score for a car with a price of $33,000? b. What is a Z score for a car with a price of $30,000?
Answer:
a) Z = 2.86
b) Z = 2
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 23000, \sigma = 3500[/tex]
a. What is a Z score for a car with a price of $33,000?
This is Z when X = 33000. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{33000 - 23000}{3500}[/tex]
[tex]Z = 2.86[/tex]
b. What is a Z score for a car with a price of $30,000?
This is Z when X = 30000. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{30000 - 23000}{3500}[/tex]
[tex]Z = 2[/tex]
if u can do all 3 that will be great, TYSM!!
A: Five people each paying $14.50 means that the total bill was [tex]5\cdot\$14.50=\boxed{\$72.50}.[/tex]
B: Subtract the number of people he already has from the number of people he needs to get [tex]42-29=\boxed{13}[/tex] people.
C: Divide 96 by 8 to get [tex]\boxed{12}[/tex] packs.
Arithmetic is where it all begins, y'know?
Answer:
Hope this helps though I m not sure about the first one since I got another answer 72.5 but it isn't there
The radius of a circle is 6.5cm What is the diameter
The diameter of a circle is twice the radius.
Diameter = radius x 2
= 6.5 x 2
= 13 cm
Answer:
13
Step-by-step explanation:
diameter is two times the radius
6.5 x 2 = 13
Explain how you will solve the pair of equations by substitution.show all steps and write the solution in (x,y) form.
Answer:
(-2, -3)Step-by-step explanation:
The question is incomplete. Here is the complete question.
Consider the following pair of equations:
y = 3x + 3 ... 1
y = x − 1 ... 2
Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form .
From both equations, we will substitute y = 3x+3 in equation 1 into 2 to have;
3x+3 = x-1
collecting the like terms;
3x-x = -1-3
2x = -4
Dividing both sides by 2 will give;
2x/2 = -4/2
x = -2
Substituting x = -2 into equation 1;
y = 3x+3
y = 3(-2)+3
y = -6+3
y = -3
The solution in (x, y) form is (-2, -3)
A car travels at an average speed of 48 miles per hour. How long it take to travel 156 miles
Answer:
3.25 h = 3 h 15 m
Step-by-step explanation:
156 mi * 1h/48 mi = 3.25 h = 3 h 15 m
Answer: 195 min or 3 hr and 15 min
Step-by-step explanation:
We can set up a proportion to solve this problem.
[tex]\frac{48mi}{60 min} =\frac{156 mi}{x}[/tex]
[tex]48x=156*60[/tex]
[tex]48x=9360[/tex]
[tex]x=195 min[/tex]
We can also write this in terms of hours and minutes.
[tex]\frac{60 min}{1 hr} =\frac{195 min}{x}[/tex]
[tex]60x=195[/tex]
[tex]x=3.25[/tex]
3 hr and 15 min
Use a graphing calculator to sketch the graph of the quadratic equation, and then state the domain and range y=2x^2-x+3
Answer:
For the domain since we have a quadratic function then the domain would be all the real numbers:
[tex] D =[x | x \in R][/tex]
And if we want to find the range we can find the vertex:
[tex] v_x = -\frac{b}{2a}= -\frac{-1}{2*2}= \frac{1}{4}[/tex]
And now we can find th coordinate of y of the vertex like this:
[tex] f(V_x) = 2(\frac{1}{4})^2 -(1/4) +3 =2.875[/tex]
And then the range would be:
[tex] R=[x \geq 2.875][/tex]
Step-by-step explanation:
We have the following function given:
[tex] y = 2x^2 -x +3[/tex]
For this case we can plot the function with a calculator and we got the plot in the figure attached.
For the domain since we have a quadratic function then the domain would be all the real numbers:
[tex] D =[x | x \in R][/tex]
And if we want to find the range we can find the vertex:
[tex] v_x = -\frac{b}{2a}= -\frac{-1}{2*2}= \frac{1}{4}[/tex]
And now we can find th coordinate of y of the vertex like this:
[tex] f(V_x) = 2(\frac{1}{4})^2 -(1/4) +3 =2.875[/tex]
And then the range would be:
[tex] R=[x \geq 2.875][/tex]
What’s the correct answer for this question?
Answer:
E : x=12
Step-by-step explanation:
ACCORDING TO THE THEOREM
(PD)(PC) = (AP)(PB)
8(3+x)=10x
24+8x=10x
24=10x-8x
24 = 2x
x = 12
Answer:
12
Step-by-step explanation:
PD * PC = AP * PB
= 8 * (3 + x) = 10 * x
= 24 + 8x = 10x
= 10x - 8x = 24
= 2x = 24
= 12
A stock's price fluctuations are approximately normally distributed with a mean of $104.50 and a standard deviation of $23.62. You decide to purchase whenever the price reaches its lowest 10% of values. What is the most you would be willing to pay for the stock?
a) $80.88
b) $74.23
c) $84.62
d) $134.77
Answer:
[tex]P(z<\frac{a-\mu}{\sigma})=0.10[/tex]
and we can set up the following equation
tex]z=-1.282<\frac{a-104.5}{23.62}[/tex]
And if we solve for a we got
[tex]a=104.5 -1.282*23.62=74.22[/tex]
And the best answer for this case would be:
b) $74.23
Step-by-step explanation:
Let X the random variable that represent the stocks price of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(104.5,23.62)[/tex]
Where [tex]\mu=104.5[/tex] and [tex]\sigma=23.62[/tex]
For this part we want to find a value a, such that we satisfy this condition:
[tex]P(X>a)=0.90[/tex] (a)
[tex]P(X<a)=0.10[/tex] (b)
As we can see on the figure attached the z value that satisfy the condition with 0.10 of the area on the left and 0.90 of the area on the right it's z=-1.282. On this case P(Z<-1.282)=0.10 and P(z>-1.282)=0.90
If we use condition (b) from previous we have this:
[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.10[/tex]
[tex]P(z<\frac{a-\mu}{\sigma})=0.10[/tex]
and we can set up the following equation
tex]z=-1.282<\frac{a-104.5}{23.62}[/tex]
And if we solve for a we got
[tex]a=104.5 -1.282*23.62=74.22[/tex]
And the best answer for this case would be:
b) $74.23
A shop sells boxes of chocolate. In total there are 252 dark chocolate and 180 milk chocolates.if every box is identical,how many boxes could there be?
Answer:
12 boxes.
Step-by-step explanation:
We need to find the greatest common factor of 251 and 180:
First find the prime factors :
252 = 2*2*3*3*7
180 = 2*2*3*3*5
So the GCF = 2*2*3*3 = 36.
So id each box is identical, there could be 7 boxes of dark chocolates and 5 boxes of milk chocolates each containing 36 chocolates.
Total number of boxes = 12.
2x + 3y = 12
Complete the missing value in the solution to the equation.
1,8)
Answer:
Step-by-step explanation:
[tex]\mathrm{Slope-Intercept\:form\:of}\:2x+3y=12:\quad y=-\frac{2}{3}x+4\\\mathrm{Domain\:of\:}\:-\frac{2}{3}x+4\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}\\\mathrm{Range\:of\:}-\frac{2}{3}x+4:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<f\left(x\right)<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}[/tex]
[tex]\mathrm{Parity\:of}\:-\frac{2}{3}x+4:\quad \mathrm{Neither\:even\:nor\:odd}\\\mathrm{Axis\:interception\:points\:of}\:-\frac{2}{3}x+4:\quad \mathrm{X\:Intercepts}:\:\left(6,\:0\right),\:\mathrm{Y\:Intercepts}:\:\left(0,\:4\right)\\\mathrm{Inverse\:of}\:-\frac{2}{3}x+4:\quad -\frac{3x-12}{2}\\\mathrm{Slope\:of\:}-\frac{2}{3}x+4:\quad m=-\frac{2}{3}[/tex]
A well is 7 meters deep, and a snail climbs up from the bottom of the well.It climbs 3meters during the day and falls 2 meters at night.How many days can the snail crawl out of the well?
Answer:
1
Step-by-step explanation:
The balance on Taylor's credit card is $2000 it has an interest rate of 12.5% she wants to compare the difference between paying $75 and $100 of the monthly balance how much does she save in interest and fees if she pays $100 instead of $75?
Answer:
so she saved 82 cents in the interest the month after
Step-by-step explanation:
case 1: payment is $75
interest on 2000 = 0.125/12×2000 = $20.83
so the actual repayment on the balance = (75-20.83) = $54.17
therefore,balance =$(2000-54.7)=$1945.83
interest in the next month = $20.27
case 2: payment is $100
interest on 2000 is still $20.83
repayment = $79.73
balance = $1920.27
interest in the next month = 20.01
so she saved 82 cents in the interest the month after
Answer:
$101
Step-by-step explanation:
Check link explanation.
Eighty percent of all California drivers wear seat belts. If three drivers are pulled over,
what is the probability that all would be wearing their seat belts? Write as a percent to the nearest tenth. Thanks!
Answer:
The probability that the three drivers would wear seat belts is 0.5
Step-by-step explanation:
Given
Percentage of drivers using seat belt = 80%
Number of drivers pulled over = 3
Required
Probability that all three drivers wore seat belt
First, the probability that a driver would wear seat belt has to be calculated.
Let's represent that with P(D)
P(D) is equivalent to the percentage of drivers using seat belt
[tex]P(D) = 80%[/tex]%
[tex]P(D) = \frac{80}{100}[/tex]
[tex]P(D) = 0.8[/tex]
Let the probability that the three drivers would wear seat belts be represented as P(All).
P(All) is calculated as thus;
(Probability that the first driver would wear seat belt) and (Probability that the second driver would wear seat belt) and (Probability that the first driver would wear seat belt).
Mathematically, this means
[tex]P(All) = P(D) * P(D) * P(D)[/tex]
Substitute [tex]P(D) = 0.8[/tex]
[tex]P(All) = 0.8 * 0.8 * 0.8[/tex]
[tex]P(All) = 0.512[/tex]
[tex]P(All) = 0.5[/tex] --- Approximated
Hence, the probability that the three drivers would wear seat belts is 0.5
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
A
Step-by-step explanation:
(f-g)(x) means that the 2 functions are being subtracted.
[tex]3^{x}[/tex] +10x -(5x-3) =[tex]3^{x}[/tex] +10x-5x+3
simplify!
[tex]3^{x}[/tex] +5x+3
the answer is A
The length of time a person takes to decide which shoes to purchase is normally distributed with a mean of 8.21 minutes and a standard deviation of 1.90. Find the probability that a randomly selected individual will take less than 5 minutes to select a shoe purchase. Is this outcome unusual?
Answer:
4.55% probability that a randomly selected individual will take less than 5 minutes to select a shoe purchase.
Since Z > -2 and Z < 2, this outcome is not considered unusual.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
If [tex]Z \leq 2[/tex] or [tex]Z \geq 2[/tex], the outcome X is considered to be unusual.
In this question:
[tex]\mu = 8.21, \sigma = 1.9[/tex]
Find the probability that a randomly selected individual will take less than 5 minutes to select a shoe purchase.
This is the pvalue of Z when X = 5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5 - 8.21}{1.9}[/tex]
[tex]Z = -1.69[/tex]
[tex]Z = -1.69[/tex] has a pvalue of 0.0455.
4.55% probability that a randomly selected individual will take less than 5 minutes to select a shoe purchase.
Since Z > -2 and Z < 2, this outcome is not considered unusual.