Answer to Question #116255 in Statistics and Probability for arijit chaudhuri

Question

The probability of a telesales representative making a sale on a customer call is 0.15. find the probability that No sales are made in 10 calls and More than 3 sales are made in 20 calls

Answer 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

$X\backsim binomial(20,0.15)$

$P(X\le3)=\binom{20}{0}(0.15)^0(1-0.15)^{20}+ \\ \hspace{5 em}\binom{20}{1}(0.15)^1(1-0.15)^{19}+ \\ \hspace{5 em}\binom{20}{2}(0.15)^2(1-0.15)^{18}+ \\\hspace{5 em}\binom{20}{3}(0.15)^3(1-0.15)^{17}=0.6477\\ P(X\ge3)=1-0.6477=0.3523$

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