Question

Given a normal distribution with mu = 101 and sigma = 20. and given you select a sample of n = 16, What is the probability that X is less than 92?

Answer 1

To find the probability that X is less than 92 in a normal distribution with mu = 101 and sigma = 20, you can standardize the value 92 and use a standard normal table or calculator to find the probability. The probability is approximately 0.3277.

Step-by-step explanation:

To find the probability that X is less than 92, we need to standardize the value 92 using the formula:

z = (x - mu) / sigma

where z is the z-score, x is the value we want to find the probability for, mu is the mean, and sigma is the standard deviation. Plugging in the values, we get:

z = (92 - 101) / 20 = -0.45

Next, we can use a standard normal table or calculator to find the probability corresponding to this z-score. The probability that X is less than 92 is approximately 0.3277.