Question

According to the National Health Survey, the heights of adult males in the United States are normally distributed with mean 69.0 inches and standard deviation 2.8 inches.

(a) What is the probability that an adult male chosen at random is between 64 and 74 inches tall? (Round your answer to three decimal places.)


(b) What percentage of the adult male population is more than 6 feet tall? (Round your answer to one decimal place.)
________ %

Answer 1

Date: 11/11/2019 Answer a) The probability that an adult male chosen at random is between 64 and 74 inches tall is, First, compute the z score then find probability based on standard nommal table. For x 64 converts to Z = 64 69 2.80 =-1.786 For x 74 converts to Z = 74 69 = 2.80 -1.786

From the standard normal distribution table, the associated probability for z values and subtracts the probability is p(64 x 74) p(-1.786 z S1.786) p(z 1.786)- p(z -1.786) 0.9629 0.0370 =0.9259 0.926 The probability that an adult male chosen at random is between 64 and 74 inches tall is 0.926 b) The percentage of the adult male population is more than 6 feet tall is, First, compute the z score then find probability based on standard normal table.

Forx 6x 12 72 converts to Z = 72-69 = 2.80 =1.07 From the standard normal distribution table, the associated probability is 0.858. Since find the area to the right, so subtract from 1 to get, P(z>1.07) 1- (z <1.07) =1-0.8579 = 0.142 14.2% The probability that domestic airfares are $550 or more is 14.2%