Question

15. For a random sample of n = 64, find the probability of a sample mean being

Answer 1

Answer:

0.9726

Explanation:

The computation of the probability of a sample mean is shown below:

$P(\bar x < 24.3)$

To find the probability first we have to determine the z score which is

$z = \frac{\bar x - \mu_{\bar x}}{\sigma_{\bar x}} \\\\ = \frac{\bar x - \mu }{\frac{\sigma}{\sqrt{n} } } \\\\ = \frac{24.3 - 24}{\frac{1.25}{\sqrt{64} } }$

= 1.92

Now probability is

$P(\bar x < 24.3) \\\\= P(z < 1.92)$

= 0.9726

Hence, the probability of the sample mean is 0.9726

We simply applied the above formulas to determined the probability of a sample mean and the same is to be considered