Question

teachers’ salaries in north dakota the average teacher’s salary in north dakota is $35,441. assume a normal distribution with σ = $5100. use the standard normal distribution table. round the final answers to at least 4 decimal places and round intermediate z - value calculations to 2 decimal places.
part 1 of 2
what is the probability that a randomly selected teacher’s salary is greater than $39,200?
p(x > 39,200) = 0.2296
part: 1 / 2
part 2 of 2
for a sample of 45 teachers, what is the probability that the sample mean is greater than $36,636? assume that the sample is taken from a large population and the correction factor can be ignored.
p(\overline{x} > 36,636) = 0.0143 (try again)

Explanation:

Step1: Identify parameters for Part 2

$\mu = 35441$, $\sigma = 5100$, $n = 45$, $\bar{x} = 36636$

Step2: Calculate standard error

$\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} = \frac{5100}{\sqrt{45}} \approx \frac{5100}{6.7082} \approx 759.98$

Step3: Compute z-score

$z = \frac{\bar{x} - \mu}{\sigma_{\bar{x}}} = \frac{36636 - 35441}{759.98} \approx \frac{1195}{759.98} \approx 1.57$

Step4: Find probability from z-table

$P(Z > 1.57) = 1 - P(Z \leq 1.57) = 1 - 0.9418 = 0.0582$

Answer:

0.0582