Over the entire six years that students attend an Ohio elementary school, they are absent, on average, 28 days due to influenza. Assume that the standard deviation over this time period is σ = 9 days. Upon graduation from elementary school, a random sample of 36 students is taken and asked how many days of school they missed due to influenza. The probability that the sample mean is between 25 and 30 school days is ________.
A) 0.0228
B) 0.0918
C) 0.8860
D) 0.9082

Question

Quizplus · Accepted Answer

The probability can be found using the standard normal distribution (Z-score). The mean (μ) is 28 days, and the standard deviation (σ) is 9 days. For a sample size (n) of 36, the standard error (σ_x̄) is σ/√n = 9/√36 = 1.5 days. To find the probability that the sample mean is between 25 and 30 days, we calculate the Z-scores for these values and use the Z-table or a normal distribution calculator.Z for 25 days = (25 - 28) / 1.5 = -2. Z for 30 days = (30 - 28) / 1.5 = 1.33. Looking these up in the Z-table or using a calculator gives the probability between these Z-scores, which is approximately 0.8860.

Over the Entire Six Years That Students Attend an Ohio