Answer:
a. Their average weight is of 200 pounds.
b. 0.0875 = 8.75% probability that the maximum safe weight will be exceeded
c. 0.0002 = 0.02% probability that the maximum safe weight will be exceeded
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set 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]
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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
a. If 60 people are riding the coaster, and their total weight is 12,000 pounds, what is their average weight?
12000/60 = 200 pounds
Their average weight is of 200 pounds.
b. If a random sample of 60 adult men ride the coaster, what is the probability that the maximum safe weight will be exceeded?
Men means that [tex]\mu = 189, \sigma = 63[/tex].
Sample of 60 means that [tex]n = 60, s = \frac{63}{\sqrt{60}} = 8.13[/tex]
Safe weight will be exceeded if the sample mean is above 200 pounds, which has probability of 1 subtracted by the pvalue of Z when X = 200. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{200 - 189}{8.13}[/tex]
[tex]Z = 1.35[/tex]
[tex]Z = 1.35[/tex] has a pvalue of 0.9115
1 - 0.9115 = 0.0875
0.0875 = 8.75% probability that the maximum safe weight will be exceeded.
c. If a random sample of 60 adult women ride the coaster, what is the probability that the maximum safe weight will be exceeded?
Women means that [tex]\mu = 165, \sigma = 76[/tex]
Sample of 60 means that [tex]n = 60, s = \frac{76}{\sqrt{60}} = 9.81[/tex]
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{200 - 165}{9.81}[/tex]
[tex]Z = 3.57[/tex]
[tex]Z = 3.57[/tex] has a pvalue of 0.9998
1 - 0.9998 = 0.0002
0.0002 = 0.02% probability that the maximum safe weight will be exceeded
URGENT I'll give you stars, brainliest answer, or slide into ur dms for this answer pls9^(x2)=y in log form
Answer:
log ( 28 )
13 √ 25
log
( 1/ 2 )
Step-by-step explanation:
To solve this, we will use this property of logarithms:
If x= a ^ y
then log an (x) = y, where a is the base
So if e^9 = y , or y = e^9
then log e (y) = 9
NB: log e (y) is also referred to as the natural log of y, or ln y.
So it can also be written as:
Answer: ln y = 9, or log e (y) = 9
There are six orange marbles, 2 red marbles, 3 white marbles, and 4 green marbles in a bag. Once a marble is drawn, it is replaced. Find the probability of each outcome.
1.) a red then white marble
2.) a white then green marble
3.) two orange marbles in a row
4.) a red then an orange then a green marble
Answer:
2.) 2 orange marble in a raw
Step-by-step explanation:
because there are more orange marble than other colours
a publisher for a promising new novel figures fixed costs overhead, advances, promotion, copy editing, type setting and so on at $57,000 and variable costs printing, paper, binding, shipping at $2.90 for each book produced. If the book is sold to distributors for $10 each, how many must be sold to break even?
Answer:
$2.90 for each book produced. If the book is sold to distributors for $10 each, how many must be sold to break even?
Step-by-step explanation:
. citizen of the represented state
Rosa is making a poster that has a rainbow as part of the design. Using a compass she draws a semicircle with a radius of 18 cm. She draws another semicircle that has a radius of 12 cm as shown. What is the area of the shaded part of the rainbow?
Answer:
282.7 cm²
Step-by-step explanation:
Hello There!
To find the area of the shaded area we are going to want to find the area of the whole semi circle and subtract it by the area of the smaller semi circle
To find the area of a semicircle we use this formula
[tex]A=\frac{\pi r^2}{2}[/tex]
where r = radius
For the large semi circle
The radius of the larger semi circle is 18 cm so we plug in 18 into r in the formula
So..
[tex]A=\frac{\pi 18^2}{2} \\18^2=324\\324\pi =1017.87602\\\frac{1017.87602}{2} =508.9380099[/tex]
So the area of the whole semi circle is 508.9380099 cm²
Now to find the area of the smaller semi circle
The radius for the smaller semi circle is 12 cm so we plug in 12 into r in the formula
[tex]A=\frac{12^2\pi }{2} \\12^2=144\\144\pi =452.3893421\\\frac{452.3893421}{2} =226.1946711[/tex]
so the area of the smaller semi circle is 226.1946711cm²
Finally we want to subtract the area of the smaller semi circle from the area of the whole semi circle
508.9380099 - 226.1946711 = 282.7433388
Finally we want to round to the nearest tenth and we get that the area of the rainbow is 282.7 cm²
Can someone tell me if the answers i entered are correct ?? If not please tell me whats right
Answer:
theyre correct
Step-by-step explanation:
HELP PLS
find the value of x
Answer:
x = 5
Step-by-step explanation:
These angles are supplementary so:
9x + 12x + 75 = 180
21x + 75 = 180
21x = 180 - 75
21x = 105
x = 5
Jason bought 12 new CDs to add to his
collection. The next day, his baby
brother went into his room and
scratched half of his CDs. He now only
has 56 working CDs left. How many
CDs did Jason start with?
Answer:
He had origanlly had 68 altogether
Step-by-step explanation:
Because if u count the scrateched ones which was 6 is now 62 then add the other six because there was 12 and his brother scrateched half which is basically 12 / 2 = 6 so if u add the six is 68
What Im basically saying is 56 + 12 = 68
The number of people I don’t know amusement park triples every hour. This morning, there were 20 people at the muse meant park when it opened. Now, there are 4860 people have them use meant park. Write an equation to represent the number of hours the amusement park has been open.
Answer:
equation is y=20(3)^x
Step-by-step explanation:
example:
Solve for x over the integers:
20 (3)^x = 4860
Divide both sides by 20:
3^x = 243
243 = 3^5:
3^x = 3^5
Equate exponents of 3 on both sides:
Answer:
x = 5 hours open with 4860 guest
I’m not sure which one to pick on this quiz and could us the help
Answer:
[tex]f^-1(x)=2x+12[/tex]
Step-by-step explanation:
What is 43% of 166? (Round to the nearest whole number)
NEED HELP FAST‼️ WILL MARK B‼️‼️‼️
Triangle ABC has the following coordinates. A(6,-6), B(3,-3) and C(6,-3). What are the
coordinates of triangle A'B'C' if it is dilated with a scale factor of 4 with the origin as the center of
dilation?
Answer:
4×6=24,4×-6=-24,4×3=12,4×-3=-12,4×
6=24,4×-3=-12
There are 50 pieces of candy and 15 gum balls what is the ratio
15-year old students
a) How many 15-year old
students took part in
the survey?
(1)
b) How many more 15-year
old students than 11-year
old students spent
between 35 and 45 mins
on social media?
(1)
Total marks: 2
10 20 30 40 50 60 70 80
Time (mins)
Next Question
Which number has the greatest value -17, -24 ,0, 23?
Answer:
23
Step-by-step explanation:
Example:
You have no money, you decide to swipe your credit card to purchase something for $17. Again, you did so for another item paying $24. You are now $41 in debt. Your mom decides to pay for your debt which is $41. You decide to actually go to your part-time job and earn $23. When was the time you had the most money in this example? When you earned the $23 becuase you started with none.
Answer:
23
Step-by-step explanation:
Out of the numbers given:
All positive numbers are greater than negative numbers.
This eliminates -17 and -24.
Comparing 0 to 23:
23 has more value than 0.
0 < 23
This means out of the numbers given, 23 has the greatest value.
Hope this helps.
Point O is the center of the square ABCD. Point E is the midpoint of line segment CD. The area of square ABCD is 24, what is the are of the quadrilateral BCEO?
Answer: You divided 24 by 3 then you take the answer
Step-by-step explanation:I hope it help
HELP MEEEEEEE PLEASE
Answer:
14m
Step-by-step explanation:
The expression that shows the number of coupon books:
14*m = 14m
Answer:
14m
Step-by-step explanation:
they say the members are represented by M, and the members sold 14 coupon we can't say it is m + 14 so the answer is 14m
At Pizza Pi, 40% of the pizzas made last week had extra cheese. If 8 pizzas had extra cheese, how many pizzas in all were made last week?
Answer:
20 pizzas.
Step-by-step explanation:
40% = 8
1% = 8 ÷ 40 = 0.2
100% = 0.2 x 100 = 20
What methods could you use to calculate the x-coordinate of the midpoint of
a horizontal segment with the endpoints of (-20, 0) and (20, 0)?
A. divide 0 by 20
B. divide 2 by 20
- C. calculate the average of the x-coordinates
D. take the average of the endpoints
M
E. divide 20 by 2
Answer:
c
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
Gina earns an hourly rate of $8.94 for a 40-hour week. She receives
double-time (2 times the hourly rate) for any weekend work. This week
she worked his regular 40 hours plus 10 hours on Saturday. Calculate her
gross pay.
Answer: $536.40
Step-by-step explanation:
8.94 * 2 = 17.88
8.94(40) + 17.88(10)
357.60 + 178.80 = $536.40
CAN SOMEONE PLEASE HELP
Answer:
99°
Step-by-step explanation:
Triangle=180°
Given, 41+40=81
180-81
Answer:
99°
Step-by-step explanation:
Sum of angles in a triangle is supplementary,
x + 41° + 40° = 180°
x + 91° = 180°
x = ( 180 - 91 )
x = 99°
A gift card has a total value of $50. Jane has already used $24 of it. Write and solve an equality to show how much more she can spend.
Answer: 26
Step-by-step explanation:
50-24=26
Find the 110 term of the sequence -7,3, 13, 23, ..
Answer:
1083
Step-by-step explanation:
The formula for the nth term of a sequence is a+(n - 1 )d, where a is the first term and d is the difference between each term. Here, a is -7 and d is 10 (terms go up by ten each time).
So, the nth term = -7+(n-1)10 = -7+10n-10 = 10n-17
So, the 110th term = 10(110)-17=1100-17=1083
What is the range of the set of data points given below? 175 159 180 172 163 166 170 162 175 157 178 160
Answer:
Range = highest observation - lowest observation
180-157 = 23
Answer:
Hi! The answer to your question is 23
Step-by-step explanation:
☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
☆Brainliest is greatly appreciated!☆
Hope this helps!!
- Brooklynn Deka
If it takes 2 pounds of batter to make 5 sheets of cookies ,how many pounds of batter will it take to make 27 sheets of cookies?
Answer:
6666666
Step-by-step explanation:
6
Answer:
12 pounds of batter
Step-by-step explanation:
27/5 =5.4
change 5.4 to 6
6 x 2 =12
12 pounds of batter
help me...................
Answer:
A. 4
Step-by-step explanation:
The answer to this question is option A. which is 4. This is because for every value of 5 or above, we round up to the next digit. For option B and C, those values are either 5 or above. This means that choosing those values would give a new value of 74.16, not 74.15 as the answer is showing.
You are testing the claim that the mean GPA of night students is different from the mea GPA of day students. You sample 20 night students, and the sample mean GPA is 2.84 with a standard mean GPA is 2.55 with a standard deviation of 0.45. Test the claim using a 1% level of significance. Assume the population standard deviations are unequal and that GPAs are normally distributed. Give answer to at least 4 decimal places. What are the correct hypotheses
Answer:
As the calculated value of z does not lie in the critical region the null hypothesis is accepted that the GPA mean of the night students is the same as the GPA mean of the day students.
Step-by-step explanation:
Here n= 20
Sample mean GPA = x`= 2.84
Standard mean GPA = u= 2.55
Standard deviation = s= 0.45.
Level of Significance.= ∝ = 0.01
The hypothesis are formulated as
H0: u1=u2 i.e the GPA of night students is same as the mean GPA of day students
against the claim
Ha: u1≠u2
i.e the GPA of night students is different from the mea GPA of day students
For two tailed test the critical value is z ≥ z∝/2= ± 2.58
The test statistic
Z= x`-u/s/√n
z= 2.84-2.55/0.45/√20
z= 0.1441
As the calculated value of z does not lie in the critical region the null hypothesis is accepted that the GPA mean of the night students is the same as the GPA mean of the day students.
classes
3. Jeff, Lorri, and Dan had a race.
In how many different ways
could they come in first, second,
and third?
Answer:
6 different ways.
Step-by-step explanation:
(1) Jeff, Lorri, Dan
(2) Jeff, Dan, Lorri
(3) Lorri, Jeff, Dan
(4) Lorri, Dan, Jeff
(5) Dan, Jeff, Lorri
(6) Dan, Lorri, Jeff
O GEOMETRY, MEASUREMENT, DATA ANALYSIS
Metric conversion with decimal values: Two-step problem
A coral reef grows 0.17 m every week. How much does it grow in 13 weeks?
Write your answer in centimeters.
cm
X Х
5
?
Meters to centimeters
Answer:
It grows 221 centimeters in 13 weeks.
Step-by-step explanation:
Each meter has 100 centimeters.
A coral reef grows 0.17 m every week
So it grows 0.17*100 = 17 cm every week.
How much does it grow in 13 weeks?
17 cm every week for 13 weeks, so
17*13 = 221
It grows 221 centimeters in 13 weeks.
This grid shows where a squirrel hid different nuts which ordered pair shows wheee the squirrel hid the acorns
2,8
2,10
8,2
8,8
A figure is shown.
8x
7x
44.4°
What is the measure, in degrees, of the highlighted angle?
We know that the sum of a straight line is 180° . So here there are 3 angles in a straight line . And the sum is 180° . So that ,
[tex]\tt\to Sum_{(angles \ of \ a \ straight \ line)}= 180^o \\\\\tt \to 7x + 8x + 44.4^o = 180^o \\\\\tt\to 15x = 180^o - 44.4^o \\\\\tt\to 15x = 135.6^o \\\\\tt\to x =\dfrac{135.6^o}{15}\\\\\tt\to \boxed{\orange{\tt x = 9.04^{\circ} \approx 9^{\circ} }}[/tex]
So the measure of angle that is highlighted will be 8x = 8(9) = 72°
Answer:
72.32degrees
x is 9.04
Step-by-step explanation:
7×9.04=63.28
8×9.04=72.32
44.4+63.28+72.32=180