Question

The mean height of women in a country​ (ages 20minus​29) is 64.2 inches. A random sample of 75 women in this age group is selected. What is the probability that the mean height for the sample is greater than 65 ​inches? Assume sigmaequals2.84. The probability that the mean height for the sample is greater than 65 inches is nothing.

Answer 1

Answer:

$z=\frac{65-64.2}{\frac{2.84}{\sqrt{75}}} = 2.440$

And we can find the probability using the complement rule and with the normal standard table like this:

$P(Z>2.440) =1-P(Z<2.440) = 1-0.993 =0.007$

The probability that the mean height for the sample is greater than 65 inches is 0.007

Step-by-step explanation:

Let X the random variable that represent the women heights of a population, and we know the following parameters

$\mu=64.2$ and $\sigma=2.84$

We are interested on this probability

$P(X>65)$

Since the sample size selected is 75>30 we can use the centrel limit theorem and the appropiate formula to use would be the z score given by:

$z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

If we find the z score for 65 inches we got:

$z=\frac{65-64.2}{\frac{2.84}{\sqrt{75}}} = 2.440$

And we can find the probability using the complement rule and with the normal standard table like this:

$P(Z>2.440) =1-P(Z<2.440) = 1-0.993 =0.007$

The probability that the mean height for the sample is greater than 65 inches is 0.007