Question

Assume that​ women's heights are normally distributed with a mean given by mu equals 63.4 in​, and a standard deviation given by sigma equals 1.9 in.
​(a) If 1 woman is randomly​ selected, find the probability that her height is less than 64 in.
​(b) If 31 women are randomly​ selected, find the probability that they have a mean height less than 64 in.

Answer 1

Solution :

Given that ,

mean =   = 63.4

standard deviation = σ   = 1.9

n = 1

= 63.4

=  / n =1.9 / 1=1.9

P( <64 ) = P[( - ) / < (64-63.4) /1.9 ]

= P(z <0.32 )

Using z table  

= 0.6255   

probability=0.6255

(B)   

n = 31

= 63.4

=  / n =1.9 / 31=0.3413

P( <64 ) = P[( - ) / < (64-63.4) /0.3413 ]

= P(z <1.76 )

Using z table  

= 0.9608

probability=0.9608