Sam is a 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) which he sells x appliances. For a random sample of 240 days, Sam had the following sales record. Assume the sales record is representative of the population of all sales for a day. Round all calculations to three decimal places.

X	0	1	2	3	4	5	6	7
F	9	72	63	41	28	14	8	5

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

(x)	Frequency	P(x)
0	9
1	72
2	63
3	41
4	28
5	14
6	8
7	5

(b) Compute the probability that x is between 2 and 5 (P(2 or 3 or 4 or 5)).

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

(d) Find the expected value for this probability distribution.

(e) Explain the expected value in the context of the problem.

(f) Find the variance and standard deviation for this probability distribution.

(g) There are several days where Sam sells 1 or 2 appliances. What are some tips you would give Sam to increase the number of appliances he is able to sell each day?