Question

A population of values has a normal distribution with μ=242.5 and σ=47.8. A random sample of size n=75 is drawn. Find the probability that a sample of size n=75 is randomly selected with a mean greater than 251.3. Round your answer to four decimal places. P(M>251.3)=

Answer 1

To find the probability of a sample mean greater than 251.3, calculate the z-score using the formula (x - μ) / (σ / √n). Then, use a Z-table or calculator to find the area to the right of the z-score.

Step-by-step explanation:

To find the probability that a sample of size 75 has a mean greater than 251.3, we can use the normal distribution formula.

The z-score is calculated as (x - μ) / (σ / √n), where x is the mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Plugging in the given values, we get z = (251.3 - 242.5) / (47.8 / √75).

Using a Z-table or a calculator, we can find the area to the right of this z-score, which represents the probability of a sample mean greater than 251.3.

The probability is approximately 0.2700.