Question

Answer the following questions given the following scenario (Be sure to show all work):   A large retail company encourages its employees to to get customers to apply for the store credit card. Below is a distribution for the number of credit card applications (X) received per employee for an 8-hour shift.

X	0	1	2	3	4	5
P(X)	0.23	0.32	0.20	0.15	0.08	0.02

1. What is the mean for the probability distribution?

2.  What is the variance for the probability distribution?

3.  What is the standard deviation for the probability distribution?

4. A producer plans an outdoor regatta for April 28th. The cost of the regatta is $9,000. This includes advertising, security, printing tickets, entertainment, etc. The producer plans to make $15,000 profit if all goes well. However, it it rains, the regatta will be cancelled. According tothe weather report, the probability of rain is 0.35. Find the producer's expected profit.

5. Three out of four American adults under age 35 have eaten pizza for breakfast. If a random sample of 10 adults under age 35 is selected, find the probability that exactly 7 have eaten pizza for breakfast.

Answer 1

Ans:

X	0	1	2	3	4	5	Total
P(X)	0.23	0.32	0.2	0.15	0.08	0.02	1
X.P(X)	0	0.32	0.4	0.45	0.32	0.1	1.59
(X-mean)2	2.53	0.35	0.17	1.99	5.81	11.63
(X-mean)2*P(X)	0.58	0.11	0.03	0.30	0.46	0.23	1.72

1)Mean==0*0.23+1*0.32+2*0.2+3*0.15+4*0.08+5*0.02=1.59

2)Variance==(0-1.59)²*0.23+(1-1.59)²*0.32+(2-1.59)²*0.2+(3-1.59)²*0.15+(4-1.59)²*0.08+(5-1.59)²*0.02=1.72

3)Standard deviation==1.31