For the dataset shown here, what portion of the data is within two standard devi
ID: 3431410 • Letter: F
Question
For the dataset shown here, what portion of the data is within two standard deviations of the mean? Express as a decimal.
0
0
2
5
10
23
49
0
0
3
6
11
23
49
0
0
3
6
11
24
51
0
1
3
6
12
24
52
0
1
3
7
12
30
59
0
1
3
7
15
35
75
0
1
3
10
15
35
100
0
1
4
10
16
38
150
0
1
5
10
20
38
170
0
2
5
10
20
46
250
Mean: 22.60
Standard Deviation: 41.85
0
0
2
5
10
23
49
0
0
3
6
11
23
49
0
0
3
6
11
24
51
0
1
3
6
12
24
52
0
1
3
7
12
30
59
0
1
3
7
15
35
75
0
1
3
10
15
35
100
0
1
4
10
16
38
150
0
1
5
10
20
38
170
0
2
5
10
20
46
250
Mean: 22.60
Standard Deviation: 41.85
Explanation / Answer
three standard deviations of the mean:
mean -3*standard deviation =22.6-3*41.85 =-102.95
mean +3*standard deviation=22.6+3*41.85=148.15
So the portion of the data is within three standard deviations of the mean is
P(-102.95<X<148.15) = P((-102.95-22.6)/41.85 <(X-mean)/s <(148.15-22.6)/41.85)
=P(-3<Z<3)
=0.9973 (from standard normal table)