A certain successful restaurant operates with a waiting line, without reservations. The managers want to know how much t

[answerhappygod]

A certain successful restaurant operates with a waiting line,
without reservations. The managers want to know how much time in
minutes (variable X) are the customers waiting and decide to
run a simple study. Before this study, the distribution
of X was completely unknown. During a specific day, a
total of 80 customers were asked to measure the waiting time.
Initially, a sample of 40 measurements (lunch) was obtained:
23.9
21.5
27.0
0.0
30.9
9.3
22.2
29.3
5.8
0.0
20.9
17.5
25.1
29.1
27.1
6.2
15.8
21.9
25.0
13.9
21.7
16.7
13.9
19.6
23.0
8.0
11.1
18.0
28.6
18.6
9.1
34.3
1.1
21.0
10.3
23.2
7.1
5.2
36.4
18.4
a) Based on this sample, compute a confidence interval for
the mean of X, for a confidence level of 95%. (10
points)
b) A new batch of 40 measurements arrives in the evening
(dinner), allowing for a sample size increase (n = 80).
Compute a new interval estimate for the mean, for the same
confidence level of 95%, taking both the lunch and the dinner
measurements into account (n = 80). (5 points)
32.9
35.5
33.7
43.4
39.0
29.0
38.0
32.7
35.3
22.0
38.4
31.5
25.5
39.4
41.7
22.1
36.3
42.3
33.7
29.4
0.0
36.5
32.5
29.2
30.6
34.7
11.2
34.5
8.7
23.2
36.7
19.2
33.4
44.0
39.2
33.7
15.7
26.5
0.0
46.5
c) Compare your answers to 2.1 and 2.2 and justify the
difference(s). In your opinion, should the managers attempt to
obtain separate interval estimates for lunch and dinner?
Justify. (5 points)
d) Assuming the standard deviation of the population is
equal to the sample standard deviation (sample of 80 measurements),
determine the sample size required for a confidence interval with a
margin of error of 3 minutes and a confidence level of 95%. (5
points)