A normally distributed population has a mean of 500 and a standard deviation of 60. Determine the probability that a random sample of size 16 selected from this population will have a sample mean less than 475.
A) 0.3251
B) 0.7124
C) 0.0475
D) 0.0712

Question

Quizplus · Accepted Answer

The probability that a sample mean is less than a certain value can be found using the Z-score formula for a sample mean: Z = (X̄ - μ) / (σ/√n), where X̄ is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. Here, Z = (475 - 500) / (60/√16) = -25 / (60/4) = -25 / 15 = -1.67. Looking up -1.67 on the Z-table gives a probability of approximately 0.0475, indicating the probability that a random sample of size 16 will have a sample mean less than 475.

A Normally Distributed Population Has a Mean of 500 and a Standard