Question

The Apple, Inc. sales manager for the Chicago West Suburban region is disturbed about the large number of complaints her office is receiving about defective ipods. New Apple CEO Tim Cook is also very displeased and wants the situation remedied as soon as possible.

The sales manager examines this Excel file ipod Weekly Complaints, which shows the number of complaints concerning defective ipods received by her office for each of the immediately preceding 52 weeks.

Question 1. Make a histogram of the number of complaints received each week. As your bin range use the values 60, 80, 100, 120, 140, 160 listed in the Excel file. Then select the choice below that is the most appropriate conclusion from the histogram (2 submissions allowed).

The histogram is severely left-skewed; therefore a normal model is not appropriate to describe the number of complaints received each week.The histogram has several outliers; therefore a normal model is not appropriate to describe the number of complaints received each week.     Based on the histogram, it is appropriate to use a normal model to describe the distribution of the number of complaints received each week.The histogram appears to be bi-modal; therefore a normal model is not appropriate to describe the number of complaints received each week.The histogram is severely right-skewed; therefore a normal model is not appropriate to describe the number of complaints received each week.

Question 2.What is the probability that between 77 and 114 complaints are received in one week? Use a N(108,20) model to approximate the distribution of weekly complaints.

ANSWERL .5573

Question 3. Tim Cook decrees that the next time the number of complaints received in one week exceeds the value of the third quartile Q₃, he will register a strong complaint with the ipod assembly plant in China. What is the value of Q₃? (Note: as in question 2, use a N(108,20) model to approximate the distribution of weekly complaints). Use 1 decimal place in your answer.

Q₃.

Weekly Count of Complaints Concerning Defective ipods: Chicago West Suburban Region
Week Number	Number of complaints
1	80
2	119			bin range
3	114			60
4	107			80
5	144			100
6	115			120
7	106			140
8	104			160
9	97
10	99
11	50
12	124
13	111
14	76
15	115
16	94
17	133
18	117
19	87
20	117
21	145
22	86
23	85
24	125
25	105
26	117
27	143
28	64
29	116
30	102
31	87
32	108
33	65
34	113
35	124
36	84
37	131
38	87
39	126
40	127
41	121
42	98
43	114
44	87
45	102
46	129
47	90
48	118
49	103
50	87
51	120
52	126

Answer 1

Question 1. Make a histogram of the number of complaints received each week. As your bin range use the values 60, 80, 100, 120, 140, 160 listed in the Excel file. Then select the choice below that is the most appropriate conclusion from the histogram (2 submissions allowed).

set up the histogram in Excel, using data-->data analysis--->histogram

get this

We can see that the histogram is approximately bell shaped

ans: Based on the histogram, it is appropriate to use a normal model to describe the distribution of the number of complaints received each week.

Question 2.What is the probability that between 77 and 114 complaints are received in one week? Use a N(108,20) model to approximate the distribution of weekly complaints.

Note: N(108,20) indicates that the distribution is normal with mean = 108 and variance = 20 (that is, the standard deviation is ) (The notation is always ). However, looking at the answer provided, it is being assumed that the original notation is and hence the standard deviation is 20 )

Let X be the number of complaints received on any given week. We can say that X is normally distributed with mean and standard deviation

the probability that between 77 and 114 complaints are received in one week is

ANSWER the probability that between 77 and 114 complaints are received in one week is 0.5573

Question 3. Tim Cook decrees that the next time the number of complaints received in one week exceeds the value of the third quartile Q₃, he will register a strong complaint with the ipod assembly plant in China. What is the value of Q₃? (Note: as in question 2, use a N(108,20) model to approximate the distribution of weekly complaints). Use 1 decimal place in your answer.

note: again, assuming that the notation is and not N(108,20)

Let X be the number of complaints received on any given week. We can say that X is normally distributed with mean and standard deviation

Let Q3 be the value of the third quartile. That is, the probability that less than Q3 complaints are received in any given week is 0.75

First we will find the z value corresponding to the probability 0.75

Using the standard normal tables, we can get for z=0.67,

P(Z<0.67) = 0.75

However, we need

We can equate the z score of Q3 to 0.67 and get

ans: Q₃ = 121.4