(3.46) Here are the IQ test scores of 31 seventh-grade girls in a Midwest school

Question

(3.46) Here are the IQ test scores of 31 seventh-grade girls in a Midwest school district:

Data Set

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:

Step 2:
Does your stemplot show departures from Normality?

Step 3:
Nonetheless, proportions calculated from a Normal distribution are not always very accurate for small numbers of observations.
Find the mean for these IQ scores.
Give your answer to 2 decimal places.
Fill in the blank:

Step 4:
Find the standard deviation for these IQ scores.
Give your answer to 2 decimal places.
Fill in the blank:

Step 5:
What proportions of the scores are within one standard deviation of the mean?
Give your answer to 2 decimal places.
Fill in the blank:

Step 6:
What proportions of the scores are within two standard deviations of the mean?
Give your answer to 2 decimal places.
Fill in the blank:

Step 7:
What would these proportions be in an exactly Normal distribution?

(3.46) Here are the IQ test scores of 31 seventh-grade girls in a Midwest school district:

Data Set

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:

Stemplot II 7 24 7 0 8 0 8 69 9 13 9 68 10 23334 10 578 11 11222444 11 89 12 12 8 13 2 Stemplot III 7 240 8 069 9 1368 10 023334578 11 1122244489 12 08 13 02 Stemplot IV 7 24 7 8 8 69 9 13 9 68 10 023334 10 578 11 11222444 11 89 12 0 12 8 13 02 Stemplot I 7 24 8 69 9 13 9 68 10 023334 10 578 11 1122244489 12 08 13 02

Step 2:
Does your stemplot show departures from Normality?

The stemplot is symmetric with two peaks. There are two low outliers, but the stemplot looks reasonably Normal. No, the stemplot looks Normal. The stemplot shows an uneven distribution with no definite peak.

Step 3:
Nonetheless, proportions calculated from a Normal distribution are not always very accurate for small numbers of observations.
Find the mean for these IQ scores.
Give your answer to 2 decimal places.
Fill in the blank:

Step 4:
Find the standard deviation for these IQ scores.
Give your answer to 2 decimal places.
Fill in the blank:

Step 5:
What proportions of the scores are within one standard deviation of the mean?
Give your answer to 2 decimal places.
Fill in the blank:

Step 6:
What proportions of the scores are within two standard deviations of the mean?
Give your answer to 2 decimal places.
Fill in the blank:

Step 7:
What would these proportions be in an exactly Normal distribution?

0.32 and 0.84 0.68 and 0.95 0.68 and 0.997 0.84 and 0.95

Explanation / Answer

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Stem-and-Leaf Display: C1

Stem-and-leaf of C1 N = 31
Leaf Unit = 1.0

2 7 24
2 7
2 8
4 8 69
6 9 13
8 9 68
14 10 023334
(3) 10 578
14 11 11222444
6 11 89
4 12 0
3 12 8
2 13 02

There are two low outliers, but the stemplot looks reasonably Normal.

the standar D. is

the mean:105.84

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