A research concludes that the number of hours of exercise per week for adults is

Question

A research concludes that the number of hours of exercise per week for adults is normally distributed with a mean of 4 hours and a standard deviation of 3 hours. Show all work. Just the answer, without supporting work, will receive no credit.

(a) Find the 75th percentile for the distribution of exercise time per week. (round the answer to 2 decimal places)

(b) What is the probability that a randomly selected adult has more than 7 hours of exercise per week? (round the answer to 4 decimal places)

Explanation / Answer

a. P(X>x)=0.75

Using z table we get P(Z>z)=0.75, so z =-0.674

So z=x-mu/sd=x-4/3=-0.674

So x=-0.674*3+4=1.978

b. P(x>7)=P(z>7-4/3)=P(z>1)=0.1587

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