Probability of randomly selecting a sample of 50 one-bedroom apartments in this town and getting a sample mean of less than $780 is 0.0002
Explanation:Average cost, μ = $830
Sample size, n = 50
Standard deviation, σ = $100
The sample mean is to be less than $780
X = 780
Calculate the z-value
[tex]\begin{gathered} z=\frac{X-\mu}{\frac{\sigma}{\sqrt[]{n}}} \\ z=\frac{780-830}{\frac{100}{\sqrt{50}}} \\ z=-3.54 \end{gathered}[/tex]P(X < 780) = P(z < -3.54)
From the normal distribution table:
P(z < -3.54) = 0.0002
Probability of randomly selecting a sample of 50 one-bedroom apartments in this town and getting a sample mean of less than $780 is 0.0002
