1
APPLYING PROBABILITY DISTRIBUTIONS
Lisa Ayers
Walden University
Professor: Kaplan
Stat 2002
10/29/2023
2
APPLYING PROBABILITY DISTRIBUTIONS
1. A market-research firm was hired to determine the percentage of people in a market area
who would purchase a client's magazine if a door-to-door sales campaign were
undertaken. The firm stated that 40% would buy if contacted at home. Suppose the
marketing company has tried the sales campaign at 300 randomly selected homes.
Assuming the market research was done properly and the 40% is representative, how
many sales are expected if the publisher attempts to sell to 5,000 homes?
If the market research was done properly, and 40% represents the true probability of
purchase, we can use the binomial distribution formula to find the expected number of
sales if the publisher attempts to sell to 5,000 homes. Expected Sales = (Probability of
purchase) x (Number of homes) Expected Sales = (0.40) x (5,000) = 2,000 sales. So, if
the campaign is conducted with 5,000 homes, the expected number of sales is 2,000.
If the market research was accurate, what is the probability that fewer than 100
individuals will buy? Use the normal approximation to the binomial.
To find the probability that fewer than 100 individuals will buy, we can use the normal
approximation to the binomial distribution because the number of trials (5,000) is large, and the
probability of
success (0.40) is not too small or too large First, calculate the mean (μ) and standard
deviation (σ) of the binomial distribution:@
μ = n * p@
@ @= 5,000 * 0.40@
@ @ = 2,000@
σ = √(n * p * (1 - p))@ @
@= √(5,000 * 0.40 * 0.60)@
@≈ 40
