The Apple, Inc. sales manager for the Chicago West Suburban region is disturbed

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 2.What is the probability that between 77 and 120 complaints are received in one week? Use a N(108,20) model to approximate the distribution of weekly complaints.

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.

Explanation / Answer

Question 2)

Let X = the number of complaints received in one week

We need to find P(77 < X < 120) for a Gaussian Normal distribution with mean = 108 and SD = 20

Converting the X values to Z scores :

Z = 77 - 108 / 20 = -35/20 = -1.75

Thus, X = 77 for a N(108,20) is equivalent to Z = -1.75 for a N(0,1)

Z = 120 - 108 / 20 = 12/20 = 0.6

Thus, X = 77 for a N(108,20) is equivalent to Z = 0.6 for a N(0,1)

So, we need to find P(-1.75 < Z < 0.6) = P(Z < 0.6) - P(Z < -1.75)

Referring to the standard normal Z-table :

P(-1.75 < Z < 0.6) = 0.7257 - 0.0401

P(-1.75 < Z < 0.6) = 0.6856

Ans : Thus, the probability that between 77 and 120 complaints are received in one week = 0.6856

Question 3)

By definition, the third quartile Q3 is that score that is greater than 75% of all scores in the distribution. From the standard normal Z table, we see that a value of Z = 0.67 is greater than 75% of all scores which makes Z = 0.67 the 75th percentile score or the Q3 score.

To convert Z to X -->

0.67 = X - 108 / 20

13.4 = X - 108

X = 121.4

Ans : Q3 = 121.4

Cheers!

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