The number of students using the ATM on campus daily is normally distributed with a mean of 237.6 and a standard deviation of 26.3.For a random sample of 55 days,what is the probability that the ATM usage averaged more than 230 students per day?
A)0.9756
B)0.9483
C)0.9838
D)0.9524

Question

Quizplus · Accepted Answer

We can use the central limit theorem to approximate the sampling distribution of the sample mean. Since the sample size is large enough (n>30), we can assume that the sampling distribution of the sample mean is normal with a mean of 237.6 and a standard deviation of 26.3/sqrt(55) = 3.543.

To find the probability that the ATM usage averaged more than 230 students per day, we need to standardize the sample mean and calculate the z-score.

z = (230 - 237.6) / 3.543 = -2.14

Using a standard normal table or calculator, we can find the area to the right of z = -2.14:

P(z > -2.14) = 0.9838

Therefore, the probability that the ATM usage averaged more than 230 students per day is 0.9838 or approximately 0.98. The answer is C.

The Number of Students Using the ATM on Campus Daily