11. A research concludes that the number of hours of exercise per week for adult

Question

11. 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) 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)

(b) Find the 80th percentile for the distribution of exercise time per week. (round the answer to 2 decimal places)

Explanation / Answer

here we use standard normal variate z=(x-mean)/sd

(a) answer is 0.1587

for x=7, z=(7-4)/3=1

P(x>7)=P(z>1)=1-P(z<1)=1-0.8413=0.1587

P(z<1)=0.8413 ( using ms-excel normsdist(1))

(b) answer is 7.84

P(Z<z)=0.8 and corresponding z=1.2816 ( using ms-excel=normsdist(0.8)

now x=4+3*1.2816=7.84 ( two decimal approximation)

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