Question

Given a normal population whose mean is 635 and whose standard deviation is 74, find the probability that a random sample of 5 has a mean between 651 and 664

A) 0.2154
B) 0.4602
C) 0.5398
D) 0.7846

Answer 1

To find the probability that a random sample of 5 has a mean between 651 and 664, calculate the z-scores for both values and find the probabilities associated with those z-scores using a standard normal distribution table.

Step-by-step explanation:

To find the probability that a random sample of 5 has a mean between 651 and 664, we need to calculate the z-scores for both values and then find the probabilities associated with those z-scores using a standard normal distribution table.

Step 1: Find the z-score for 651: z = (651 - 635) / (74 / √5) = 1.949

Step 2: Find the z-score for 664: z = (664 - 635) / (74 / √5) = 2.649

Step 3: Find the probability associated with z = 1.949 and z = 2.649 using a standard normal distribution table. The probability is the difference between the two probabilities: P(1.949 < z < 2.649) = P(z < 2.649) - P(z < 1.949) = 0.9978 - 0.9744 = 0.0234