Question

The mean height of women in a country​ (ages 20−​29) is 64.2 inches. A random sample of 50 women in this age group is selected. What is the probability that the mean height for the sample is greater than 65​ inches? Assume σ equals=2.58. Round to four decimal places.

Answer 1

Solution :

Given that,

mean = = 64.2

standard deviation = = 28

n=50

= =64.2

= / n = 28/ 50 = 3.96

P( > 65) = 1 - P( <65 )

= 1 - P[( - ) / < (65-64.2) /3.96 ]

= 1 - P(z <0.20 )

Using z table

= 1 - 0.5793

= 0.4207

probability= 0.4702