DATA: Student What is your gender? How old are you? What is your height in inche
ID: 2933702 • Letter: D
Question
DATA:
Student
What is your gender?
How old are you?
What is your height in inches?
What is your cumulative Grade Point Average (GPA) at FTCC or your primary college?
How many hours do you sleep each night?
1
Male
20
68
3.67
6
2
Female
18
56
3.8
7
3
Female
43
67
3.89
7
4
Female
27
64
3.7
6
5
Female
22
67
3.4
7
6
Female
31
67
3.55
8
7
Female
22
64
2.5
6
8
Female
26
67
2.05
7
9
Male
38
71
0
8
10
Female
25
65
3.5
6
11
Female
28
65
4
4
12
Female
19
63
4
6
13
Female
17
65
0
7
14
Male
17
71
2
9
15
Male
33
68
3
7
16
Female
31
65
4
8
17
Female
19
55
2.5
7
18
Female
25
58
3
8
19
Male
30
69
3.82
7
20
Female
20
64
3.2
6
21
Female
31
69
3.78
6
22
Male
49
70
4
4
23
Female
23
52
2.5
6
24
Female
27
67
2.8
8
25
Male
18
69
0
6
26
Female
41
63
4
6
27
Female
25
60
3
6
28
Male
17
65
3.8
6
29
Female
17
66
4
6
30
Female
30
67
3.82
5
31
Male
17
72
3.44
6
32
Male
19
71
4
7
33
Male
29
56
3.75
4
34
Male
28
68
3.5
7
35
Male
29
69
1.9
8
36
Male
50
73
2.87
6
37
Female
16
67
4
8
38
Female
34
66
3.2
6
39
Female
38
65
4
6
40
Female
24
63
3.2
6
41
Female
34
66
3.2
6
42
Female
19
66
3.68
8
43
Female
24
63
3
7
44
Female
21
63
2.3
5
45
Female
51
66
3
5
46
Female
18
61
3.9
8
47
Male
36
71
2
6
48
Female
20
64
2
7
49
Male
20
69
3
8
50
Female
22
62
2.8
8
51
Female
17
67
0
8
52
Female
25
59
3
8
Question:
Height of Adults in US - Height of adults are known to be normally distributed with a mean of 69 inches and a standard deviation of 2.5 inches
Find the following: (Round each probability to four decimal places)
Find the probability that a randomly selected adult US adult has a height less than 64 inches tall.
Find the mean of the heights that I collected from statistics students at FTCC. Use data set. (Round to one decimal place.)
Find the probability that a random sample of 52 adults would have a mean height that is less the value from #2 above.
Find the following values:
Find the z score for #1 and #3 in part A above (Round each to the nearest hundredth.)
Find the height, x-value, for each percentile: Low 15%, Top 10%, and Middle 90%. (Round each to the nearest tenth.)
Student
What is your gender?
How old are you?
What is your height in inches?
What is your cumulative Grade Point Average (GPA) at FTCC or your primary college?
How many hours do you sleep each night?
1
Male
20
68
3.67
6
2
Female
18
56
3.8
7
3
Female
43
67
3.89
7
4
Female
27
64
3.7
6
5
Female
22
67
3.4
7
6
Female
31
67
3.55
8
7
Female
22
64
2.5
6
8
Female
26
67
2.05
7
9
Male
38
71
0
8
10
Female
25
65
3.5
6
11
Female
28
65
4
4
12
Female
19
63
4
6
13
Female
17
65
0
7
14
Male
17
71
2
9
15
Male
33
68
3
7
16
Female
31
65
4
8
17
Female
19
55
2.5
7
18
Female
25
58
3
8
19
Male
30
69
3.82
7
20
Female
20
64
3.2
6
21
Female
31
69
3.78
6
22
Male
49
70
4
4
23
Female
23
52
2.5
6
24
Female
27
67
2.8
8
25
Male
18
69
0
6
26
Female
41
63
4
6
27
Female
25
60
3
6
28
Male
17
65
3.8
6
29
Female
17
66
4
6
30
Female
30
67
3.82
5
31
Male
17
72
3.44
6
32
Male
19
71
4
7
33
Male
29
56
3.75
4
34
Male
28
68
3.5
7
35
Male
29
69
1.9
8
36
Male
50
73
2.87
6
37
Female
16
67
4
8
38
Female
34
66
3.2
6
39
Female
38
65
4
6
40
Female
24
63
3.2
6
41
Female
34
66
3.2
6
42
Female
19
66
3.68
8
43
Female
24
63
3
7
44
Female
21
63
2.3
5
45
Female
51
66
3
5
46
Female
18
61
3.9
8
47
Male
36
71
2
6
48
Female
20
64
2
7
49
Male
20
69
3
8
50
Female
22
62
2.8
8
51
Female
17
67
0
8
52
Female
25
59
3
8
Explanation / Answer
Height of Adults in US - Height of adults are known to be normally distributed with a mean of 69 inches and a standard deviation of 2.5 inches
Find the following: (Round each probability to four decimal places)
Find the probability that a randomly selected adult US adult has a height less than 64 inches tall.
Answer : Pr(X < 64 inch) = Pr( X < 64 inch ; 69 inch; 2.5 inch)
Z = (64 - 69)/2.5 = -2
Pr(X < 64 inch) = Pr( X < 64 inch ; 69 inch; 2.5 inch) = Pr(Z < -2) = 0.0228
Find the mean of the heights that I collected from statistics students at FTCC. Use data set. (Round to one decimal place.)
Mean of the sample height = 65.3 inch
Find the probability that a random sample of 52 adults would have a mean height that is less the value from #2 above.
Answer : Standard error of the sample mean = / sqrt(n) = 2.5/ sqrt(52) = 0.3467
Pr(x < 65.3 ) = Pr(x < 65.3; 69; 0.3467)
Z = (65.3 - 69)/ 0.3467 = -10.67
Find the following values:
Find the z score for #1 and #3 in part A above (Round each to the nearest hundredth.)
Z#1 = -2
Z#2 = -10.67
Find the height, x-value, for each percentile: Low 15%, Top 10%, and Middle 90%. (Round each to the nearest tenth.)
Low 15%
so Pr(X <x ; 69; 2.5) = 0.15
so Z value for p = 0.15 is
Z = -1.0364
(x - 69)/2.5 = -1.0634
x = 69 - 2.5 * 1.0634 = 66.34 inch
Top 10%
Pr(X <x ; 69; 2.5) = 1 - 0.10 = 0.90
so Z value for p = 0.90 is
Z = 1.28
(x - 69)/2.5 = 1.28
x = 69 + 2.5 * 1.28 = 72.2 inch
Middle 90%
90% interval = 69 +- 1.96 * 2.5 = (64.1 inch, 73.9 inch)
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