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

Step-by-step 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 :-

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

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