The time taken by Nick to do his statistics homework follows a normal distribution with a mean of 25 minutes and a standard deviation of 5 minutes. Jasmin’s homework time also follows a normal distribution with a mean of 50 minutes and a standard deviation of 10 minutes. They hate each other’s guts and never work together so we can assume that Nick’s homework completion is independent of Jasmine’s homework completion.

a) Define the random variable D to be the difference between the amount of time spent on a randomly selected assignment of Jasmin’s and a randomly selected assignment of Nick’s. So D = N – J. Find the mean and the standard deviation of D.

b) Calculate the probability that Nick spent longer doing his assignment than Jasmin did. Show your method clearly.

Answer:

a) Mean of D = -25

Standard deviation of D = 11.18

b) P(N > J ) = 0.9875

Step-by-step explanation:

Given - μₙ = 25, σₙ = 5 , μₐ = 50 , σₐ = 10

where μₙ is mean of nick and  μₐ is mean of jasmine

 σₙ = 5 is standard deviation of nick and σₐ is standard deviation of jasmine

To find - a) Define the random variable D to be the difference between the      amount of time spent on a randomly selected assignment of Jasmine’s and a randomly selected assignment of Nick’s. So D = N – J. Find the mean and the standard deviation of D.

b) Calculate the probability that Nick spent longer doing his assignment than Jasmine did. Show your method clearly.

Proof -

a)

Mean of D = Mean of nick - Mean of jasmine

                  = 25 - 50 = -25

standard deviation of D = √Standard deviation of Nick + jasmine

                                       = √5² + 10² = √25 + 100 = √125 = 11.18

∴ we get

Mean of D = -25

Standard deviation of D = 11.18

b)

We have to find - P(N > J)

If N > J , then D > 0

Now,

The z-score is expressed as

z = [tex]\frac{0 - (-25)}{11.18} = \frac{25}{11.18} = 2.24[/tex]

Now,

P(N>J) = P (D > 0) = P(Z < 2.24)

                            = 0.9875

⇒P(N > J ) = 0.9875

2- Mert 423 sayfalık kitabın 7
_
9

sini okumuş. Oku-madığı kac sofa kalmıştır?​

the product of 8 and a number is 25 less than twice that number. find the number​

Find the number that belongs
in the green box.
160°
3

What is the slope of the line below? If necessary, enter your answer as a
fraction in lowest terms, using the slash (/) as the fraction bar. Do not enter
your answer as a decimal number or an equation. (-6,3) (12,6)

4. Etkinlik
Ağaç sevgisini anlatan bir şiir yazınız​

is 13/10 irrational or rational

hcf of 14 154 and 28​

Find the exact length of the third side.
10
24

what number is opposite of -524

Simplify the expression 1 + 4.25n + 3/2p -3 + (-2p) + 5/4n

What is the mean absolute deviation of the following set of data?
4
6
6
2.

What is 3 percent of 1600

How many groups of two are in six

Lines s and t are parallel. Find the value of x.
PLEASE HELPPPPP, THANKSS!!!!

A box filled with 6 blue cards 6 brown carts and 6 green cards a card is chosen at random from the box what is the probability that it is a blue or green card write your answer as a fraction in simplest form

a department store sells a pair of shoes with an 87% markup, if the store bought the pair of shoes for 55.25, what is the selling price to the nearest dollar?

is every relation a function?

Rearrange the equation so a is the independent variable 9q - 4 = 3r - 6

7.
The expression 25(1.12)m represents a population of spiders after m months. Since a year hus
12 months, 25(1.12)12n represents the population of spiders after n years.
Which expression is approximately equivalent to 25(1.12)1207
A 25(2.44)"
B 25(3.90)"
с 25(13.12)
D 25(13.44)"

please help me with this question

pls help plsssssssssssssssssssssssssssssssssss

A bag of candies contains 5 red candies, 7 purple candies, and 3 green candies. What is the probability that a candy picked
at random is green?

If a regular polygon has 72 sides and an order of 72,what is the polygon’s rotational angle?

a) John wants to buy a house and is trying to figure out how much money he needs for the down payment. If the house
costs $275,000 and the down payment is 15% of the price of the house, how much will the down payment be? $

Will the sum of 56+ (-56) be Positive negative or zero

Quizziz help 9th grade please please please

Select the correct answer. What is the value of x in 2 (5x) = 14

el preocceso de 231x123

There are (3^5)^2 . 30 leaves on a tree. What is the total number of leaves on the tree? (5 points)

which statement correctly descibes what happens to the shape and location of the graph of y=2x^2 if it is regraphed as y=-1/2x^2

HELPPPPPPP