Question

Assuming the sample represents the population very well, that is, the population has approximately the same mean and same standard deviation.

a) 68% of the population fall between ___ inches and ___ inches

b) 95% of the population fall between ___ inches and ___ inches

c) 99.7% of the population fall between ___ inches and ___ inches

Height of 5 yr old Females
44.5
45.4
39.6
45.5
42
44.5
39.5
42.3
44
37.7
42.4
43
44.7
43.3
42.2
37.6
43.6
44.6
35.9
34.6
42.2
43.4
36.5
41.2
38.5
42.2
41.3
40.5
43.7
42.4
46.2
44.7
42.7
40.5
43.6
40.3
38.8
37.4
48.1
42.7
45.7
38.6
40.6
44.4
40.6
48.5
41.9
44.5
38.7
47
44.8
41.6
47.5
42.6
45
41.6
40.3
40.7
46
42.8
43.3
50.2
48.4
42
40.7
41.7
42.1
38.2
43.4
39.9
39.5
46.9
37.5
40.3
36.3
38.9
41.9
42.6
44.6
42.3

Answer 1

Solution:

Assuming the sample represents the population very well, that is, the population has approximately the same mean and same standard deviation.

From given data, we have

Mean = 42.22375

SD = 3.13099

We know the empirical rule. It states as below:

About 68% of the population falls between 1 standard deviation from mean.

Mean – 1*SD = 42.22375 - 1*3.13099 = 39.09276

Mean + 1*SD = 42.22375 + 1*3.13099 = 45.35474

About 95% of the population falls between 2 standard deviation from mean.

Mean – 2*SD =42.22375 - 2*3.13099 =35.96177

Mean + 2*SD = 42.22375 + 2*3.13099 =48.48573

About 99.7% of the population falls between 3 standard deviation from mean.

Mean – 3*SD =42.22375 - 3*3.13099 =32.83078

Mean + 3*SD =42.22375 + 3*3.13099 = 51.61672

a) 68% of the population falls between 39.1 inches and 45.4 inches.

b) 95% of the population falls between 36.0 inches and 48.5 inches.

c) 99.7% of the population falls between 32.9 inches and 51.6 inches.