Question

The average cost to rent a single-family home in Port St. Lucie is $1,256 per month. Assume that the distribution of the monthly rent of all single-family homes in Port St. Lucie is normally distributed with a standard deviation of $85. Use this information to determine the following probabilities. Round solutions to four decimal places, if necessary. Find the probability that a random sample of 63 homes in Port St. Lucie has a mean rent greater than $1,242. P(xˉ>1242) = ?

Answer 1

To find the probability that a random sample of 63 homes in Port St. Lucie has a mean rent greater than $1,242, we can use the z-score formula.

Step-by-step explanation:

To find the probability that a random sample of 63 homes in Port St. Lucie has a mean rent greater than $1,242, we need to use the z-score formula. The formula for calculating the z-score is: z = (x - μ) / (σ / sqrt(n)), where x is the sample mean, μ is the population mean, σ is the standard deviation, and n is the sample size. In this case, x = $1,242, μ = $1,256, σ = $85, and n = 63. Substituting these values into the formula, we get: z = (1242 - 1256) / (85 / sqrt(63)). Using a z-table or a calculator, we can find the probability associated with this z-score, which represents the probability that a random sample of 63 homes in Port St. Lucie has a mean rent greater than $1,242.