Question

Assume that​ women's heights are normally distributed with a mean given by μ=63.5 in​, and a standard deviation given by σ=2.1 in.

​(a) If 1 woman is randomly​ selected, find the probability that her height is less than 64 in.

​(b) If 44 women are randomly​ selected, find the probability that they have a mean height less than 64

Answer 1

Solution :

Given that ,

mean = = 63.5

standard deviation = =2.1

P(x < 64) = P(( x -) / (64-63.5) / 2.1)

= P(z < 0.24)

Using z table

= 0.5948

b.

n = 44

= 63.5

=  / n = 2.1/ 44=0.32

P( <64 ) = P[( - ) / < (64-63.5) /0.32 ]

= P(z < 1.56)

=0.9406