Question

he dean of admissions in a large university has determined that the scores of the freshman class in a mathematics test are normally distributed with a mean of 82 and a standard deviation of 8. based on this information, what is the probability that the mean score of a sample of 64 students is at least 80?

Answer 1

To find the probability that the mean score of a sample of 64 students is at least 80, calculate the z-score, use the standard error formula, and use the standard normal distribution table.

Step-by-step explanation:

To find the probability that the mean score of a sample of 64 students is at least 80, we need to calculate the z-score and use the standard normal distribution table.

First, we calculate the standard error of the sample mean using the formula:

standard error = standard deviation / square root of sample size.

In this case, the standard error = 8 / sqrt(64)

= 8 / 8

= 1.

Then, we calculate the z-score using the formula: z = (sample mean - population mean) / standard error.

In this case, the z-score = (80 - 82) / 1

= -2.

Finally, we use the standard normal distribution table or a calculator to find the probability that the z-score is less than -2.

The probability is approximately 0.0228, which means the probability that the mean score of a sample of 64 students is at least 80 is approximately 0.9772 or 97.72%.