Question

The average rent of a one-bedroom apartment in a town is $830 per month. What is the probability of randomly selecting a sample of 50 one-bedroom apartments in this town and getting a sample mean of less than $780 if the population standard deviation is $100?

Answer 1

Answer:

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

Step-by-step 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

`\begin{gathered} z=\frac{X-\mu}{\frac{\sigma}{\sqrt[]{n}}} \\ z=(780-830)/((100)/(√(50))) \\ z=-3.54 \end{gathered}`

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