Question

homework: section 7.1
score: 8.38/25 answered: 9/25
question 10
the average ticket price for a spring training baseball game is $30.72, with a standard deviation of $7.07.
in a random sample of 40 spring training tickets, find the probability that the mean ticket price exceeds
$33. (round your answer to three decimal places)

Explanation:

Step1: Calculate the standard error

The standard error formula is $\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}$.
Given $\sigma = 7.07$ and $n = 40$, then $\sigma_{\bar{x}}=\frac{7.07}{\sqrt{40}}\approx1.117$.

Step2: Calculate the z - score

The z - score formula is $z=\frac{\bar{x}-\mu}{\sigma_{\bar{x}}}$.
Here, $\mu = 30.72$, $\bar{x}=33$. So $z=\frac{33 - 30.72}{1.117}=\frac{2.28}{1.117}\approx2.04$.

Step3: Find the probability

We want $P(\bar{X}>33)$, which is equivalent to $P(Z > 2.04)$.
Since $P(Z>z)=1 - P(Z\leq z)$, and from the standard normal table $P(Z\leq2.04)=0.9793$.
So $P(Z > 2.04)=1 - 0.9793=0.0207\approx0.021$.

Answer:

$0.021$