Answer:
the probability that the woman is taller than the man is 0.1423
Step-by-step explanation:
Given that :
the men's heights are normally distributed with mean [tex]\mu[/tex] 68
standard deviation [tex]\sigma[/tex] = 3.1
And
the women's heights are normally distributed with mean [tex]\mu[/tex] 65
standard deviation [tex]\sigma[/tex] = 2.8
We are to find the probability that the woman is taller than the man.
For woman now:
mean [tex]\mu[/tex] = 65
standard deviation [tex]\sigma[/tex] = 2.8
[tex]P(x > 68 ) = 1 - p( x< 68)[/tex]
[tex]\\ 1 -p \ P[(x - \mu ) / \sigma < (68-25)/ 2.8][/tex]
= 1-P (z , 1.07)
Using z table,
= 1 - 0.8577
= 0.1423
Thus, the probability that the woman is taller than the man is 0.1423
