Question

The mean height of 15 to 18-year-old males from Chile from 2009 to 2010 was 170 cm with a standard deviation of 6.28 cm. Male heights are known to follow a normal distribution. Let X = the height of a 15 to 18-year-old male from Chile in 2009 to 2010. Then X ~ N(170, 6.28).

Suppose a 15 to 18-year-old male from Chile was 176 cm tall from 2009 to 2010. The z-score when x = 176 cm is z = . (round to nearest hundredth).

This z-score tells you that x = 176 cm is  standard deviations to the  (right or left) of the mean of ______  .

Answer 1

Solution :

z = (x - $\mu$ ) / $\sigma$ = (176 - 170) / 6.28 = 0.96

The z-score when x = 176 cm is z = 0.96

This z-score tells you that x = 176 cm is  standard deviations to the right of the mean of 170 .