Question

The height of women ages​ 20-29 is normally​ distributed, with a mean of 64.2 inches. Assume σ=2.7 inches. Are you more likely to randomly select 1 woman with a height less than 66.3 inches or are you more likely to select a sample of 14 women with a mean height less than 66.3​inches? Explain.

Answer 1

Solution :

Given that,

mean = = 64.2

standard deviation = = 2.4

(A)n = 1

=64.2

=  / n = 2.4/ 1=2.4

P( <66.3 ) = P[( - ) / < (66.3-64.2) /2.4 ]

= P(z <0.88 )

Using z table  

= 0.8106

probability=0.8106

(B)

n = 14

=64.2

=  / n = 2.4/ 14=0.6414

P( <66.3 ) = P[( - ) / < (66.3-64.2) /0.6414]

= P(z <3.27 )

Using z table  

= 0.9995

probability=0.9995