Answer to Question #145928 in Statistics and Probability for Gervas

Question

1. The probability of telesales representative making a sale on a customer call is 0.15. Find the probability that
(a) no sales are made in 10 calls, (2 marks) (b) more than 1 sales are made in 20 calls. (3 marks)
Representatives are required to achieve a mean of at least 5 sales each day.
(c) Find the least number of calls each day a representative should make to achieve this requirement. (1 mark) (d) Calculate the least number of calls that need to be made by a representative for the probability of at least 1 sale to exceed 0.95. (3 marks)

Answer 1

1)$X=$ A telesales representative making a sale on a customer call

$X\backsim binomial(10,0.15)$

$P(X=0)=\binom{10}{0}(0.15)^0(1-0.15)^{10}=0.1969$

The probability that No sales are made in 10 calls 0.1969

2)

$X\backsim binomial(20,0.15)$

$P(X\le1)=\binom{20}{0}(0.15)^0(1-0.15)^{20}+\\ \hspace{5 em}\binom{20}{1}(0.15)^1(1-0.15)^{19}=0.1755\\ P(X>1)=1-0.1755=0.8245$

The probability that more than 3 sales are made in 20 calls 0.3523

3) n* 0.15=5

n = 33.33$\approx$ 33

4)1 - P(X = 0) > 0.95 

1 -(0.85)ⁿ> 0.95

(0.85)ⁿ<0.05

n>18.4

n=19