Below is a stemplot of the IQ test scores of 74 seventh-grade students. This dis

Question

Below is a stemplot of the IQ test scores of 74 seventh-grade students. This distribution is very close to Normal: the mean is approximately 111 and the standard deviation us approximately 11. It includes all the seventh graders is a rival school except for four how outliers who were dropped because they may have been ill or otherwise not paying attention to the test. Take the Normal distribution with mean 111 and standard 11 as a description of the grade students. Use this distribution and the rule to the following question. What percentage of scores for seventh-graders are more than 100?

Explanation / Answer

mean = 111 , sd = 11

a) 100 is 1 sd below mean   {100 = 111-11}

we know by 68-95-99.7 rule

that probbaility of x between 1 sd within mean = 0.68

hence

P(100 < X< 111 +11) = 0.68

P(100 < X< 111) = 0.34    {symmetric about mean)

P(X >100) = P(100 <X<111) +P(X > 111)

                 = 0.34+0.5=0.84           {as P(X > 111) = 0.5   ,symmetric about mean , hence P(X > mean ) = 0.5}

0.84 is correct

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