Question
In: Statistics and Probability
3. The time spent commuting from home to work for all employees of a very large...
3. The time spent commuting from home to work for all employees of a very large company has a normal distribution with a mean of 43.4 minutes and a standard deviation of 12.1 minutes. Calculate the probability that the mean time spent commuting from home to work by a sample of 21 employees will be in between 43.26 and 49.35.
Solutions
Expert Solution
Solution :
Given that,
mean = 
= 43.4
standard deviation = 
= 12.1
n = 21
=
= 43.4
=
/ 
n = 12.1 /
21 = 2.64
P(43.26 < 
< 49.35)
= P[(43.26 - 43.4) / < (
-
)
/
< (49.35 - 43.4) / )]
= P( -0.05 < Z < 2.25)
= P(Z < 2.25 ) - P(Z < -0.05)
Using z table,
= 0.9878 - 0.4801
= 0.5077
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SALARY
EDUC
EXPER
TIME
39000
12
0
1
40200
10
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7
42900
12
5
30
43800
8
6
7
43800
8
8
6
43800
12
0
7
43800
12
0
10
43800
12
5
6
44400
15
75
2
45000
8
52
3
45000
12
8
19
46200
12
52
3
48000
8
70
20
48000
12
6
23
48000
12
11
12
48000
12
11
17
48000
12
63
22
48000
12
144
24
48000
12
163
12...
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