Question

A sample of size 40 is taken from a population whose mean =68, and standard deviation =12. The probability that the sample mean is larger than 70 equals

a. P(Z>70)
b. P(Z>2)
c. P(Z>1.05)
d. P(Z>0.17)

Answer 1

To find the probability that the sample mean is greater than 70, calculate the z-score and use the standard normal distribution. The correct z-score approximation is 1.05, and so the answer is c. P(Z>1.05).

Step-by-step explanation:

The question pertains to finding the probability that a sample mean is greater than 70, given a population mean of 68 and a standard deviation of 12, using a sample size of 40. To answer this question, we first need to calculate the z-score for the sample mean of 70.

The z-score is calculated using the formula:
Z = (X - μ) / (σ / √ n)
where X is the sample mean, μ is the population mean, σ is the standard deviation, and n is the sample size. Plugging in the numbers, we get:
Z = (70 - 68) / (12 / √ 40) = 2 / (12 / 6.324) ≈ 1.05.

After obtaining the z-score, we determine the probability that Z is greater than 1.05 using standard normal distribution tables or a calculator. The correct answer, therefore, is c. P(Z>1.05).