Solve the problem.
-Suppose you know that the distribution of sample proportions of fifth grade students in a large school district who read below grade level in samples of 100 students is normal with a mean of 0.30 and a standard deviation of 0.04. Suppose that you select a sample of 100 fifth grade students from this district and find that the proportion who read below grade level in the sample is 0.4. What is the probability that a second sample would be selected with a proportion less than 0.4 ?
A)0.0047
B)0.0062
C)0.9938
D)0.9953

Question

Quizplus · Accepted Answer

Given the normal distribution of sample proportions with a mean of 0.30 and a standard deviation of 0.04, a proportion of 0.4 is above the mean. The probability of selecting a second sample with a proportion less than 0.4 would include all proportions below 0.4, which is a large portion of the distribution. Since the distribution is normal and centered at 0.30, most samples will fall below 0.4, leading to a high probability, which is 0.9938.

Solve the Problem. -Suppose You Know That the Distribution of Sample Proportions of Sample