Question

Assume that the average full time college student in the U.S. requires a total of $10,500 per year to cover the costs of tutition, books and fees with a standard deviation of $1,300. If 50 full time students are randomly sampled in the U.S., what is the probability that their total annual costs for tutition, books and fees exceed $550,000? Round your answer to 4 decimal places. Remember to round your z-value to 2 decimal places.

Answer 1

Answer:

$P({\displaystyle {\overline {x}}}>11,000)=0.0033$

Step-by-step explanation:

We know that the mean $\mu$ is:

$\mu=10,500$

The standard deviation $\sigma$ is:

$\sigma=1,300$

The sample size is:

$n=50$

Then the sample average ${\displaystyle {\overline {x}}}$ is:

${\displaystyle {\overline {x}}}=\frac{550,000}{50}=11,000$

In this case we look for

$P({\displaystyle {\overline {x}}}>11,000)$

We calculate the Z score.

In this case:

$Z=\frac{{\displaystyle {\overline {x}}}-\mu}{\frac{\sigma}{\sqrt{n}}}$

$Z=\frac{11,000-10,500}{\frac{1,300}{\sqrt{50}}}$

$Z=2.72$

Therefore:

$P({\displaystyle {\overline {x}}}>11,000)=P(Z>2.72)$

Looking at the normal table we have to

$P(Z>2.72)=0.0033$