(8) Sam is a representative who sells large appliances such as refrigerators and stoves. Let x = number of appliances Sam sells on a given day. Let f = frequency (number of days) pm which he sells x appliances. For a random sample of 240 days, Sam had the following sales record. [Show your work] [20 points]

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 P(x) for x = 0 to 7.

(b) Create histogram of the probability distribution of part (a). Label the histogram.

(c) Compute the probability that x is between 2 and 5 (including 2 and 5).

(d) Compute the probability that x is less than 3.

(e) Compute the expected value of the x distribution.

(f) Compute the standard deviation of the x distribution.