Question

Suppose your company has 40% share of the market. You randomly select the names of 25

purchasers of this type of product. What is the probability that between 7 and 12 of these

purchasers, inclusive, will be your customers if the normal approximation for the binomial

is used?

Answer 1

Let X be a number of purchases, then X ~ Bin(25, 0.4). Using normal approximation, X ~ $N(25*0.4, 25*0.4*0.6)=N(10,6)$

$P(7<X<12)=P(7<N(10,6)<12)=P(7<10+2.45N(0,1)<12)=P(-1.225<N(0,1)<0.816)=0.79275-0.11029=0.68246$