Question

1. A marathoner is now running his marathons with an average time of 3 hours, and 15 minutes, and a standard deviation of 15 minute and her times follow a normal distribution. What is the probability of the marathoner running a marathon time of exactly 2 hours and 58 minutes?
   1. 0.00
   2. 0.05
   3. 0.15
   4. 0.12

2. Which of the following would indicate a process has special causes of variation?
   1. A point is above the lower control limit and below the upper control limit
   2. There are 9 consecutive points within the control limits going up
   3. A point is above the upper control limit
   4. There are 8 consecutive points below the center line and above the lower control limit
   5. B, C, and D are correct

Use the following data for problems 10-12: Crusty’s pizza company records the number of complaints they receive on their pizzas each day. The last twenty days are in the table below.

Day	Complaints	Day	Complaints
1	6	11	12
2	1	12	5
3	4	13	2
4	4	14	8
5	9	15	1
6	2	16	4
7	12	17	14
8	5	18	18
9	9	19	12
10	2	20	7

3. The upper control limit for the number of complaints is?
   1. 14.70
   2. 11.54
   3. Does not exist
   4. 8.15

4. The process is?
   1. Is out of control because at least one point is above the upper control limit
   2. Is out of control because all the points are above the center line
   3. Is in control
   4. Out of control because at least one point is below the upper control limit

1. The center line for the number of complaints is”
   1. 0
   2. 3.94
   3. 8.48
   4. 6.85

Answer 1

ans )mean (u) = 195 minutes

standard deviation = 15 min/

P(x = 178)= )

P(x = 178) = =0.12

option D is true

ans )special cause of variation are

There are 9 consecutive points within the control limits going up

A point is above the upper control limit

There are 8 consecutive points below the center line and above the lower control limit

option E is correct

ans) since mean of the data is 6.85 and standard deviation 4.9

The upper control limit for the number of complaints is 11.54 option B is correct

ans )the process is out of control because some points lies outside the ucl and lcl

option A is correct

ans )The center line for the number of complaints is 6.85 option D is correct