The percentage of IQ scores for rural Midwest seventh-graders that would score m

Question

The percentage of IQ scores for rural Midwest seventh-graders that would score more than 100 is ______. (Give your answer as a whole number.)

The stemplot of the IQ test scores of 74 seventh-grade students is displayed.



This distribution is very close to Normal with a mean of 111 and a standard deviation of 11. It includes all seventh graders in a rural Midwest school except for 4 low outliers who were dropped because they may have been ill or otherwise not paying attention to the test. Consider the Normal distribution with a mean of 111 and a standard deviation of 11 as a description of the IQ test scores of all rural Midwest seventh-grade students.

Fill in the blank:

The percentage of IQ scores for rural Midwest seventh-graders that would score more than 100 is ______. (Give your answer as a whole number.)

Explanation / Answer

we have been given that the distribution id normal and the mean = 111

with standard deviation = 11

the formula to be used = z = (x-mean)/standard deviation

p(x>100) =

For x = 100, z = (100 - 111) / 11 = -1

Hence P(x > 100) = P(z > -1) = [total area] - [area to the left of -1]

1 - [area to the left of -1]

now from the z table we will take the value of z score = -1

    = 1 - 0.1587 = 0.8413
therefore the persentage of students getting more then 100 = 84.13%

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