Question

The mean height of women in a country​ (ages 20minus​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 sigmaequals2.58. Round to four decimal places.

Answer 1

Answer: 0.0142

Explanation:

Given : The mean height of women in a country​ (ages 20 - ​29) is 64.2 inches.

i.e.
`\mu=64.2`

Also,
`\sigma=2.58`

Sample size : n= 50

Let x denotes the height of women.

Then, the probability that the mean height for the sample is greater than 65​ inches :-

`P(x>65)=1-P(x\leq 65)\\\\=1-P((x-\mu)/((\sigma)/(√(n)))\leq(65-64.2)/((2.58)/(√(50))))\\\\=1-P(z\leq2.193)\ \ [\because z=(x-\mu)/((\sigma)/(√(n)))]\\\\=1-0.9858463\ \ [\text{By using z-value table or calculator}]\\\\=0.0141537\approx0.0142`

Hence, the the probability that the mean height for the sample is greater than 65​ inches = 0.0142