Question

The SAT scores have an average of 1,200 with a standard deviation of 200. A sample of 64 scores is selected. (Round your answers to four decimal places.) What is the probability that the sample mean will be larger than 1,222?

Answer 1

To find the probability that the sample mean will be larger than 1,222, we need to convert the sample mean into a z-score and use a standard normal distribution table or calculator.

Step-by-step explanation:

To find the probability that the sample mean will be larger than 1,222, we need to convert the sample mean into a z-score using the formula:

z = (x - µ) / (σ / √n)

where x is the sample mean, µ is the population mean, σ is the population standard deviation, and n is the sample size.

After calculating the z-score, we can use a standard normal distribution table or a calculator to find the probability.

Answer 2

To find the probability that the sample mean will be larger than 1,222, calculate the z-score and find the area under the standard normal distribution curve.

Step-by-step explanation:

To find the probability that the sample mean will be larger than 1,222, we need to calculate the z-score of the sample mean and then find the area under the standard normal distribution curve for z > (X - µ) / (σ / √n), where X is the sample mean, µ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, X = 1,222, µ = 1,200, σ = 200, and n = 64. So, the z-score is (1,222 - 1,200) / (200 / √64) = 22 / (200 / 8) = 22 / 25 = 0.88.

Using a standard normal distribution table or a calculator, we can find that the area to the right of the z-score of 0.88 is approximately 0.1882. Therefore, the probability that the sample mean will be larger than 1,222 is 0.1882 or 18.82%.