Suppose you know that the distribution of sample proportions of fifth grade stud

Question

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 0.08. 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 0.42. How many standard deviations is the sample proportion above or below the mean of the distribution of sampling proportions?

1.5 standard deviation(s) above the mean

1.43 standard deviation(s) above the mean

5.25 standard deviation(s) above the mean

0.12 standard deviation(s) above the mean

Explain how'd you got the answer please.

1.5 standard deviation(s) above the mean

1.43 standard deviation(s) above the mean

5.25 standard deviation(s) above the mean

0.12 standard deviation(s) above the mean

Explanation / Answer

Z value will be given as (x-mean)/sd

here our x will be 0.42 and mean is 0.3 and sd is 0.08

thus Z is (0.42-0.3)/0.08=1.5, since it is a +ve value therefore it is above the mean

So correct answer is A

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