In a particular large school system, the average IQ of elementaryschool children

Question

In a particular large school system, the average IQ of elementaryschool children is 105 and standard deviation is 15. A sample of 81children is randomly selected from elementary schools with thesystem. What is the probability the average IQ of the sample isbelow 108?
I first did the problem by stating the values n =81, = 105, = 15
SD(y) = / n = 15 / 81 =1.67
Then I found the z score using z = x - / = 108- 105 / 1.67 = 1.80
P(z<1.80) = 0.9641
I also thought I should subtract it from 1 which would be1-0.9641= 0.0359
I wasn't sure if I had to subtract from 1 since it said findthe sample below 108? Sometimes the problems says more or less soseeing below made me confuse. Let me know if it is correct and ifnot what I did wrong.
I first did the problem by stating the values n =81, = 105, = 15
SD(y) = / n = 15 / 81 =1.67
Then I found the z score using z = x - / = 108- 105 / 1.67 = 1.80
P(z<1.80) = 0.9641
I also thought I should subtract it from 1 which would be1-0.9641= 0.0359
I wasn't sure if I had to subtract from 1 since it said findthe sample below 108? Sometimes the problems says more or less soseeing below made me confuse. Let me know if it is correct and ifnot what I did wrong.

Explanation / Answer

Assuming your math is correct, the answer is .9641. A scoreof below 108 would be referring to all scores less 108. Thus,you would want the area to the left. This is what the p-valuegave you.

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