Question

The height of women ages​ 20-29 is normally​ distributed, with a mean of 64.9 inches. Assume stdv=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 26 women with a mean height less than 66.3 ​inches? Round to 4 decimal places

Answer 1

Solution :

Given that ,

1) P(x < 66.3)

= P[(x - ) / < (66.3 - 64.9) / 2.7]

= P(z < 0.52)

Using z table,

= 0.6985

2) = 64.9

= / n = 2.7 / 26 = 0.53

P( < 66.3) = P(( - ) / < (66.3 - 64.9) / 0.53)

= P(z < 2.64)

Using z table

= 0.9959