Question

The height of women ages​ 20-29 is normally​ distributed, with a mean of 64.4 inches. Assume sigma = 2.6 inches. Are you more likely to randomly select 1 woman with a height less than 65.8 inches or are you more likely to select a sample of 22 women with a mean height less than 65.8 ​inches? Explain.

What is the probability of randomly selecting 1 woman with a height less than 65.8 ​inches?

What is the probability of selecting a sample of 22 women with a mean height less than 65.8 ​inches?

Answer 1

Solution :

Given that ,

a.

P(X<65.8 ) = P[(X- ) / < (65.8 - 64.4) / 2.6]

= P(z < 0.54)

Using z table

probability=0.7054

b.

Solution :

Given that ,

mean = = 64.4

standard deviation = = 2.6

n = 22

= 64.4

=  / n = 2.6 / 22=0.55

P( < 65.8) = P[( - ) / < (65.8-64.4) /0.55 ]

= P(z < 2.55)

Using z table  

probability= 0.9946