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\\\\\nP(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
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