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MATH HOMEWORK HELP

1) Sam is representative who sells large appliances such as refrigerators, stoves, and so forth. Let x = number of appliances Sam sells on a given day. Let f = frequency (number of days) with which he sells x appliances. For a random sample of 240 days, Sam had the following sales record.

X 0 1 2 3 4 5 6 7

F 9 72 63 41 28 14 8 5

Assume the sales record is representative of the population of all sales days.

a) Use the relative frequency to find the p(x) for x = 0 to 7

Solution: We have the following table:

0

1

2

3

4

5

6

7

Total

9

72

63

41

28

14

8

5

240

The probability is found as:

Using the previous table we obtain the probabilities as:

0

1

2

3

4

5

6

7

Total

9

72

63

41

28

14

8

5

240

0.0375

0.3

0.2625

0.170833

0.116667

0.058333

0.033333

0.020833

b) Use a histogram to graph the possibility distribution of part (a)

Solution: We have the following Histogram:

2) Find the probability p(z<1.23)

Solution: We know that

,

wheredenotes the cumulative standard normal distribution.

3) The length of time to complete a door assembly on a automobile factory assembly line is normally distributed with mean = 6.7 minutes and standard deviation = 2.2 minutes. For a door selected at random, what is the probability the assembly line will be

a) 5 minutes or less

Solution: Letbe the random length of time to complete a door assembly. The probability we are looking for is

b) 10 minutes or less

Solution: We need to find

c) between 5 and 10 minutes

Solution: Now we need to find

d) more then 10 minutes

Solution: Finally,



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