Answer to Question #346960 in Statistics and Probability for Hlo

Question

Question 2.8 [2, 3, 3]

Suppose that a telemarketer has a 12% chance of making a sale on any given call. If the

telemarketer makes average of 5 calls per hour, calculate:

a) The probability that the telemarketer will make exactly 2 sales during the shift.

b) The probability that the telemarketer will makes more than 4 sales during the shift.

c) What is the probability that the telemarketer makes more than 2 call during two hours?

Answer 1

Let $X=$ the number of sales: $X\sim Bin(n, p)$

a)

$n=5, p=0.12, q=1-p=0.88$

$$P(X=2)=\dbinom{5}{2}(0.12)^{2}(0.88)^{5-2}$$

$$=0.098131968$$

b)

$n=5, p=0.12, q=1-p=0.88$

$$P(X>4)=P(X=5)=\dbinom{5}{5}(0.12)^{5}(0.88)^{5-5}$$

$$=0.0000248832$$

c)

$n=10, p=0.12, q=1-p=0.88$

$$P(X>2)=1-P(X=0)-P(X=1)$$

$$-P(X=2)=1-\dbinom{10}{0}(0.12)^{0}(0.88)^{10-0}$$

$$-\dbinom{10}{1}(0.12)^{1}(0.88)^{10-1}-\dbinom{10}{2}(0.12)^{2}(0.88)^{10-2}$$

$$=0.10868179372$$