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Sedbober [7]
3 years ago
8

If men's heights are normally distributed with mean 68 and standard deviation 3.1 inches, and women's heights are normally distr

ibuted with mean 65 and standard deviation 2.8 inches, if a random man and random woman are chosen, find the probability that the woman is taller than the man.
Mathematics
1 answer:
stira [4]3 years ago
6 0

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 \mu  68

standard deviation \sigma   = 3.1

And

the women's heights are normally distributed with mean \mu  65

standard deviation \sigma   = 2.8

We are to find the probability that the woman is taller than the man.

For woman now:

mean  \mu = 65

standard deviation \sigma = 2.8

P(x > 68 ) = 1 - p( x< 68)

\\ 1 -p  \ P[(x - \mu ) / \sigma < (68-25)/ 2.8]

= 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

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