Question

. A survey was conducted to measure the heights of U.S. men. In the survey, respondents...

. A survey was conducted to measure the heights of U.S. men. In the survey, respondents were grouped by age. In the 20-29 age group, the heights were normally distributed, with a mean of 69.9 inches and a standard deviation of 3.0 inches. A study participant is randomly selected. (Adapted from US. National Center for Health Statistics).

(a) Find the probability that his height is less than 66 inches.

(b) Find the probability that his height is between 66 and 72 inches

Homework Answers

Answer #1

Solution:

Given that,

= 69.9

=3.0

a ) p ( x  < 66 )

= p ( x -  / ) < ( 66 - 69.9 / 3.0 )

= p ( z < - 3.9 / 3.0 )

= p ( z < - 1.3 )

Using z table

= 0.0968

Probability = 0.0968

b ) p (66 < x  < 72 )

= p( 66 - 69.9 / 3.0 ) ( x -  / ) < ( 72 - 69.9 / 3.0)

= p ( - 3.9 / 3 < z < 2.1 / 3.0 )

= p ( - 1.3 < z < 0.7)

= p (z < 0.7 ) - p ( z < - .1.3 )

Using z table

= 0.7580 - 0.0968

= 0.6612

Probability = 0.6612

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
In a survey of a group of men, the heights in the 20-29 age group were...
In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 69.7 inches and a standard deviation of 4.0 inches. A study participant is randomly selected. Complete parts (a) through (d) below. (b) Find the probability that a study participant has a height that is between 68 and 70 inches. The probability that the study participant selected at random is between 68 and 70 inches tall is
In a survey of a group of​ men, the heights in the​ 20-29 age group were...
In a survey of a group of​ men, the heights in the​ 20-29 age group were normally​ distributed, with a mean of 68.3 inches and a standard deviation of 4.0 inches. A study participant is randomly selected. Complete parts​ (a) through​ (d) below. ​ (a) Find the probability that a study participant has a height that is less than 65 inches. The probability that the study participant selected at random is less than 65 inches tall is (......). ​(Round to...
n a survey of a group of​ men, the heights in the​ 20-29 age group were...
n a survey of a group of​ men, the heights in the​ 20-29 age group were normally​ distributed, with a mean of 69.5 inches and a standard deviation of 3.0 inches. A study participant is randomly selected. Complete parts​ (a) through​ (d) below
​ In a survey of a group of​ men, the heights in the​ 20-29 age group...
​ In a survey of a group of​ men, the heights in the​ 20-29 age group were normally​ distributed, with a mean of 68.9 inches and a standard deviation of 3.0 inches. A study participant is randomly selected. Complete parts​ (a) through​ (d) below.​(a) Find the probability that a study participant has a height that is less than 66 inches.The probability that the study participant selected at random is less than 66 inches tall is nothing . ​(Round to four...
Using the given information answer the following questions. Show work where appropriate. In a survey of...
Using the given information answer the following questions. Show work where appropriate. In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of inches 68.9 and a standard deviation of 3.0 inches. A study participant is randomly selected. Complete parts (a) through (d) below. (a) Find the probability that a study participant has a height that is less than 68 inches. (b) Find the probability that a study participant...
In a survey of a group of? men, the heights in the? 20-29 age group were...
In a survey of a group of? men, the heights in the? 20-29 age group were normally? distributed, with a mean of 67.7 inches and a standard deviation of 2.0 inches. A study participant is randomly selected. Complete parts? (a) through? (d) below. ?(a) Find the probability that a study participant has a height that is less than 68 inches. The probability that the study participant selected at random is less than 68 inches tall is nothing. ?(Round to four...
In a survey conducted by the National Center for Health Statistics, the sample mean height of...
In a survey conducted by the National Center for Health Statistics, the sample mean height of women in the United States ages 20-29 was 64.2 inches, with a standard deviation of 2.9 inches. Suppose the data is symmetric. Estimate the percent of women whose heights are between 64.2 and 67.1 inches. (Chebyshev's Thereom and/or Empirical Rule)
Men in the U.S have heights which are normally distributed with a mean of 68 inches...
Men in the U.S have heights which are normally distributed with a mean of 68 inches and a standard deviation of 2.5 inches. What percentage of men have heights between 66 inches and 69.5 inches? What height separates the shortest 6% of men from the 94% tallest men?
Heights of men and women in the U.S. are normally distributed. Recent information shows: Adult men...
Heights of men and women in the U.S. are normally distributed. Recent information shows: Adult men heights:    µ = 69.6 inches with σ = 3 inches. Adult women heights: µ = 64.1 inches with σ = 2.7 inches. 2. In a group of 150 U.S. women, approximately how many would be shorter than 63 inches? (round to the nearest whole person) Find the female height of the U.S. population that represents the 62nd percentile (to the nearest inch): Find the...
Heights of men and women in the U.S. are normally distributed. Recent information shows: Adult men...
Heights of men and women in the U.S. are normally distributed. Recent information shows: Adult men heights:    µ = 69.6 inches with σ = 3 inches. Adult women heights: µ = 64.1 inches with σ = 2.7 inches. A. 6.62 B. 0.1414 C. 0.8002 D. 5.75 E. 65 F. 79       -       A.       B.       C.       D.       E.       F.    If a woman is selected at random from...