A survey was conducted to measure the heights of U.S. women. In the survey, resp

Question

A survey was conducted to measure the heights of U.S. women. In the survey, respondents were grouped by age. In the 20–29 age group, the heights were normally distributed, with a mean of 64.3 inches and a standard deviation of 2.6 inches. A study participant is randomly selected. 1) Identify the mean (µ) 2) Identify the standard deviation () 3) Find the probability that her height is exactly 61 inches. 4) Find the probability that her height is less than 61 inches. 5) Find the probability that her height is more than 67 inches. 6) Find the probability that her height is between 61 and 67 inches. 7) Find the probability that her height is either less than 61 inches or more than 67 inches.

Explanation / Answer

A study participant is selected randomly.

1) The mean would be 64.3 inches

2) The standard deviation would be 2.6 inches

3) P(Her height is exactly 61) = 0 since the mass at a point for a continuous distribution is zero.

4) P(Her height is less that 61) = 0.1021794 [calculated using pnorm(61,64.3,2.6) in R ]

5) P( Her height is more than 67 inches) = 0.1495276 [calculated using 1- pnorm(67,64.3,2.6) in R ]

6) P( her height is between 61 and 67inches)=0.748293 [calculated using pnorm(61,64.3,2.6)- pnorm(67,64.3,2.6) in R ]

7) P(Her height is either less than 61 inches or more than 67 inches]

= 1 - P(Her height is between 61inches and 67 inches)

= 1 - 0.748293

=0.251707

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