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 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. Refer to Exhibit 7-1.The probability that the sample mean is between 25 and 30 school days is ___________.
A)0.0228
B)0.0918
C)0.8854
D)0.9082

Question

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  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. Refer to Exhibit 7-1.The probability that the sample mean is between 25 and 30 school days is ___________.
A)0.0228 
B)0.0918 
C)0.8854 
D)0.9082

Quizplus · Accepted Answer

We can use the central limit theorem to approximate the distribution of the sample mean. Given the sample size n=36, we have:

Sample mean ~ N(mean, standard error)
mean = population mean = 28
standard error = standard deviation/sqrt(n) = 11/sqrt(36) = 1.833

Now we can standardize the sample mean and calculate the z-score:

z = (sample mean - mean)/standard error
z(25) = (25 - 28)/1.833 = -1.639
z(30) = (30 - 28)/1.833 = 1.092

Using a standard normal distribution table or calculator, we can find the area under the curve between these two z-scores:

P(-1.639 < z < 1.092) = 0.8854

Therefore, the probability that the sample mean is between 25 and 30 days is 0.8854, which corresponds to choice (C).

Over the Entire Six Years That Students Attend an Ohio