Data: Student What is your gender? How old are you? What is your height in inche
ID: 3337299 • 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
Problem:
How many hours do you sleep each night? – According to the Mayo clinic, the average adult requires 7 – 8 hours of sleep each night. However, most adults have a hard time meeting that requirement. Medical studies have shown that a lack of sleep leads to health problems and cognitive impairment. The average number of hours that American adults sleep each night is 6.8 hours. The population standard deviation is 1.0 hours. (data from www.get.smarter.com) Assume the hours of sleep are normally distributed.
Find the following: (Round each probability to four decimal places.)
Find the probability that a randomly selected American adult sleep more that 7 hours a night.
Find the mean number of hours that an American Statistics student sleeps each night. Use data set. (Round to one decimal place.)
Find the probability that 52 randomly selected American adults would have a mean sleep time of less than #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 hour, x-value, for each percentile: Low 30%, Top 10%, and 80th percentile. (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
Solutions:
Find the probability that a randomly selected American adult sleep more that 7 hours a night.
Answer:
We are given that the hours of sleep follows a normal distribution.
Mean = 6.8
SD = 1
We have to find P(X>7)
P(X>7) = 1 – P(X<7)
Z = (X – Mean) / SD
Z = (7 – 6.8) / 1
Z = 0.2
P(Z<0.2) = P(X<7) = 0.579259709
P(X>7) = 1 – P(X<7)
P(X>7) = 1 – 0.579259709
P(X>7) = 0.420740291
Required probability = 0.420740291
Find the mean number of hours that an American Statistics student sleeps each night. Use data set. (Round to one decimal place.)
Answer:
From the given data, the mean number of hours that an American Statistics student sleeps each night is 6.615385 hours.
Answer = 6.6 hours
Find the probability that 52 randomly selected American adults would have a mean sleep time of less than #2 above.
Answer:
We have to find P(Xbar<6.6)
We are given n = 52
Z = (Xbar - µ) / [/sqrt(n)]
We are given
µ = Mean = 6.8
= SD = 1
n = 52
Z = (6.6 – 6.8) / [ 1/sqrt(52)]
Z = -0.2/ 0.138675
Z = -1.44222
P(Z< -1.44222) = P(Xbar<6.6) = 0.07462
Required probability = 0.07462
Find the z score for #1 and #3 in part A above (Round each to the nearest hundredth.)
Answer:
For #1
Z = (X – Mean) / SD
Z = (7 – 6.8) / 1
Z = 0.20
For #3
Z = (Xbar - µ) / [/sqrt(n)]
Z = (6.6 – 6.8) / [ 1/sqrt(52)]
Z = -0.2/ 0.138675
Z = -1.44
Find the hour, x-value, for each percentile: Low 30%, Top 10%, and 80th percentile. (Round each to the nearest tenth.)
Answer:
X = Mean + Z*SD
µ = Mean = 6.8
= SD = 1
For Low 30%
Z = -0.5244
X = 6.8 – 0.5244*1 = 6.275599
X = 6.3
For top 10%
Z = 1.281552
X = 6.8 + 1.281552*1 = 8.081552
X = 8.1
For 80th percentile
Z = 0.841621
X = 6.8 + 0.841621*1 = 7.641621
X = 7.6
(All Z values are taken from z-table or excel)
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