Answer:
Option B) 0.1587
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = $75,000
Standard Deviation, σ = $10,000
We are given that the distribution of salary of college teachers is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
Standard error due to sampling:
[tex]=\dfrac{\sigma}{\sqty{n}} = \dfrac{10000}{\sqrt{16}} = 2500[/tex]
P(average salary is more than $77,500)
P(x > 77500)
[tex]P( x > 77500) = P( z > \displaystyle\frac{77500 - 75000}{2500}) = P(z > 1)[/tex]
[tex]= 1 - P(z \leq1)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x > 77500) = 1 - 0.8413 = 0.1587 = 15.87\%[/tex]
Option B) 0.1587
