The mean annual income for people in a certain city (in thousands of dollars) is 39, with a standard deviation of 36. A pollster draws a sample of 43 people to interview. What is the probability that the Sample mean income is less than 33 (thousands of dollars)?

Question

Quizplus · Accepted Answer

To find the probability that the sample mean income is less than 33, we use the formula for the standard error of the mean: SE = σ / √n, where σ is the standard deviation and n is the sample size. Here, σ = 36 and n = 43, so SE = 36 / √43 ≈ 5.48. We then find the z-score for a sample mean of 33: z = (X̄ - μ) / SE = (33 - 39) / 5.48 ≈ -1.094. Looking up this z-score in a standard normal distribution table or using a calculator gives a probability of approximately 0.1379.

The Mean Annual Income for People in a Certain City