Answer:
1c
[tex]n = 33[/tex]
1d
[tex]n = 19[/tex]
Step-by-step explanation:
From the question we are told that
The probability of telesales representative making a sale on a customer call is [tex]p = 0.15[/tex]
The mean is [tex]\mu = 5[/tex]
Generally the distribution of sales call made by a telesales representative follows a binomial distribution
i.e
[tex]X \~ \ \ \ B(n , p)[/tex]
and the probability distribution function for binomial distribution is
[tex]P(X = x) = ^{n}C_x * p^x * (1- p)^{n-x}[/tex]
Here C stands for combination hence we are going to be making use of the combination function in our calculators
Generally the mean is mathematically represented as
[tex]\mu = n* p[/tex]
=> [tex]5= n * 0.15[/tex]
=> [tex]n = 33[/tex]
Generally 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 is mathematically represented as
[tex]P( X \ge 1) = 1 - P( X < 1 ) > 0.95[/tex]
=> [tex]P( X \ge 1) = 1 - P( X =0 ) > 0.95[/tex]
=> [tex]P( X \ge 1) = 1 - [ ^{n}C_0 * (0.15 )^0 * (1- 0.15)^{n-0}] > 0.95[/tex]
=> [tex] 1 - [1 * 1* (0.85)^{n}] > 0.95[/tex]
=> [tex] [(0.85)^{n}] > 0.05[/tex]
taking natural log of both sides
[tex]n = \frac{ln(0.05)}{ln(0.85)}[/tex]
=> [tex]n = 19[/tex]
