Question

Adult men have heights that a normally distributed with a mean of 69.5 inches and a standard deviation of 2.4 inches. Adult women have heights that a normally distributed with a mean of 63.8 inches and a standard deviation of 2.6 inches. Between a man with a height of 74 inches and a women with a height of 70 inches, who is more unusually tall within his or her respective sex ?

Answer 1

Answer:

Step-by-step explanation:

From the information given:

For Adult Men

Mean $\mu$ = 69.5

Standard deviation $\sigma$ = 2.4

observed value X = 74

For Adult Women

Mean $\mu$ = 63.8

Standard deviation $\sigma$ = 2.6

observed value X = 70

Therefore ; the values for their z  scores can be obtained in order to determine who is more unusually tall within his or her respective sex

For Adult Men :

$z = \dfrac{X- \mu}{\sigma}$

$z = \dfrac{74- 69.5}{2.4}$

$z = \dfrac{4.5}{2.4}$

z = 1.875

For Adult Women :

$z = \dfrac{X- \mu}{\sigma}$

$z = \dfrac{70- 63.8}{2.6}$

$z = \dfrac{6.2}{2.6}$

z = 2.3846

Thus; we can conclude that , the women is more unusually tall within his or her respective sex