Question

Assume that​ women's heights are normally distributed with a mean given by mu equals 64.4 in and a standard deviation given by sigma equals 2.9 in (a) If 1 woman is randomly​ selected, find the probability that her height is less than 65 in. ​(b) If 45 women are randomly​ selected, find the probability that they have a mean height less than 65

Answer 1

Solution,

Given that ,

mean = = 64.4

standard deviation = = 2.9

a) P(x < 65 ) = P[(x - ) / < ( 65 - 64.4 ) / 2.9 ]

= P(z < 0.21 )

Using z table

= 0.5832

b) n = 45

=   = 64.4

= / n = 2.9 / 45 = 0.432

P( < 65) = P(( - ) / < ( 65 - 64.4 ) / 0.432)

= P(z < 1.39 )

Using z table

= 0.9177