Question #1 The mean height of a 15 to 18-year-old male from Chile from 2009 to
ID: 3367941 • Letter: Q
Question
Question #1
The mean height of a 15 to 18-year-old male from Chile from 2009 to 2010 was 170 cm with a standard deviation of 6.2 cm. Male heights are known to follow a normal distribution. Let X = the height of a 15 to 18-year-old male from Chile from 2009 to 2010. Then X ~ N(170, 6.28).
a) Suppose a 15 to 18-year-old male from Chile was 168 cm tall from 2009 to 2010. The z-score when x=168 is ____ standard deviations to the ____(right or left) of the mean ____(What is the mean?)
B)Suppose the height of a 15 to 18-year-old male from Chile from 2009 to 2010 has a Z-score of 1.27. What is the male’s height? The z-score is 1.27 tells you that the male’s height is _____ standard deviations to the _____(right or left) of the mean.
Explanation / Answer
a) Z score = (168-170)/6.28 = -0.32
he z-score when x=168 is 0.32 standard deviations to the left of the mean 170
b) Male height = 1.27*6.28+170 = 177.98 cm
The z-score is 1.27 tells you that the male’s height is 1.27 standard deviations to the right of the mean.