Question

Please answer all parts. No need to explain your answer.

18. (3.46) Here are the IQ test scores of 31 seventh-grade girls in a Midwest school district: 14 100 104 89 102 91 114 114 103 105 108 130 120 132 128 118 119 8672 1 103 74 112 107 103 98 96 112 112 93 Data Set eBook Step 1: We expect IQ scores to be approximately Normal. Make a stemplot to check that there are no major departures from Normality. Use stems with units of tenths. Match your results: 7 24 913 9 68 Stemplot I 10 023334 10 578 11 1122244489 12 08 13 02

Answer 1

1)

stemplaot IV

2)

Thus, there are two low outliers, but the stem plot looks reasonably Normal.

3) Mean =Σx/n = 105.84

4) Std. Deviation = √(Σ(x-mean)²/(n-1)) = 14.27

5) within 1 std dev range = (mean-std dev , mean+stdev) = (91.57,120.11)

total number within this range = 23

so, proportion = 23/31 = 0.74

6) within 2 std dev range = (mean-2std dev , mean+2stdev) = (77.2959,134.3815)

total number within this range = 29

so, proportion = 29/31 = 0.94

7) in normal distribution, proportion for within 1 std dev is 0.68 and for 2 std dev is 0.95

so, answer is 0.68 and 0.95