Heights of adult American males are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches.

Heights of adult American males are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. The U.S. Marine Corps requires that males have heights between 64 inches and 78 inches. What percentage of males are eligible for the Marines based on height?

Expert Solution

µ = 69 , σ = 2.8

P(64 < x < 78)

Percentage of male which is required:

= P(64 – 69/2.8 < z < 78 – 69/2.8) [a = x-µ/σ]

= P(-1.79 < z < 3.21)

= P(z < 3.21) – P(z < 1.79)

= 0.9993 – 0.0367

= 09626 ≈ 96.26%

Percentage of heights of male = 96.36 %

Junaid answered 2 years ago

1. Adult men have heights with a mean of 69.0 inches and a standard deviation of...

1. Adult men have heights with a mean of 69.0 inches and a standard deviation of 2.8 inches. Find the z-score of a man 68.8 inches tall. (to 2 decimal places) 2. In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 56.5 inches, and standard deviation of 1.2 inches. A) What is the probability that a randomly chosen child has a height of less than 57.9 inches?...

Heights of fences are normally distributed with a mean of 52 inches and a standard deviation...

Heights of fences are normally distributed with a mean of 52 inches and a standard deviation of 4 inches. 1. Find the probability that one randomly selected fence is under 54 inches. 2. Find the probability that two randomly selected fences are both under 54 inches. 3. Find the probability that the mean height of 4 randomly selected fences is under 54 inches.

Heights of women are normally distributed with a mean of 63.8 inches and a standard deviation...

Heights of women are normally distributed with a mean of 63.8 inches and a standard deviation of 2.6 inches. a) find the probability that the height of a single randomly chosen women is less than 62 inches b) find the probability that the mean height of a sample of 16 women is less than 62 inches

Men’s heights are normally distributed with a mean of 72 inches and a standard deviation of...

Men’s heights are normally distributed with a mean of 72 inches and a standard deviation of 3.1 inches. A social organization for short people has a requirement that men must be at most 66 inches tall. What percentages of men meet this requirement? Choose the correct answer: A-2.62% B-2.59% C-2.56% D-2.68% Find the critical value of t for a sample size of 24 and a 95% confidence level. Choose the correct value from below: A-2.096 B-2.064 C-2.046 D-2.069 Construct a...

Men's heights are normally distributed with mean 68.9 in and standard deviation of 2.8 in. Women's...

Men's heights are normally distributed with mean 68.9 in and standard deviation of 2.8 in. Women's heights are normally distributed with mean 63.6 in and standard deviation of 2.5 in. The standard doorway height is 80 in. a. What percentage of men are too tall to fit through a standard doorway without bending, and what percentage of women are too tall to fit through a standard doorway without bending? b. If a statistician designs a house so that all of...

Women's heights are normally distributed with mean 64 inches and a standard deviation of 2.5 inches....

Women's heights are normally distributed with mean 64 inches and a standard deviation of 2.5 inches. (a) What percent of women are less than 60 inches tall? (b) The requirement of all Navy pilots is between 62 inches and 78 inches. What percent of women meet the Navy requirement? (c) If the Navy changed its requirement to eliminate the "shortest" 5% of all women, what would the requirement be on the lower end of the scale?

Adult men’s heights (in inches) are normally distributed with µ = 69 and σ = 2.8....

Adult men’s heights (in inches) are normally distributed with µ = 69 and σ = 2.8. Adult women’s heights (in inches) are normally distributed with µ = 64 and σ = 2.5. Members of the “Beanstalk Club” must be at least six feet (72 inches) tall. If a man is selected at random, what is the probability that he is eligible for the Beanstalk Club? If a woman is selected at random, what is the probability that she is eligible...

Heights for group of people are normally distributed with mean = 62 inches and standard deviation...

Heights for group of people are normally distributed with mean = 62 inches and standard deviation = 3.7 inches. Find the proportion, P, of people in the group whose heights fall into the following ranges. (Round your answers to four decimal places.) (a) Between 61 inches and 62 inches. P = (b) Between 53 inches and 71 inches. P = (c) Less than 71 inches. P = (d) Greater than 53 inches. P = (e) Either...

Heights for group of people are normally distributed with mean = 61 inches and standard deviation...

Heights for group of people are normally distributed with mean = 61 inches and standard deviation = 2.1 inches. Find the proportion, P, of people in the group whose heights fall into the following ranges. (Round your answers to four decimal places.) (a) Between 58 inches and 61 inches. P = (b) Between 56 inches and 66 inches. P = (c) Less than 66 inches. P = (d) Greater than 56 inches. P = (e) Either less than 56 inches...

Heights for group of people normally distributed with mean = 63 inches and standard deviation =...

Heights for group of people normally distributed with mean = 63 inches and standard deviation = 2.9 inches. Find the height, h such that about 20% of people in the group are shorter than that height. (Round the answer to the nearest tenth.) h = in. What is the percentile, p ranking for that height? p = %

Question