Question

Market research has shown that 60% of persons who are introduced to a certain product actually buy the product. A random sample of 15 persons were introduced to the product.

i. Define the variable of interest for this scenario.
ii. What probability distribution do you think best describes the situation? Why?
iii. Calculate the probability that exactly 9 will buy the product.

Answer 1

The variable of interest is the number of people who buy the product when introduced to it. The binomial distribution best describes the situation. The probability of exactly 9 people buying the product is approximately 19.60%.

Step-by-step explanation:

i. The variable of interest for this scenario is the number of persons who buy the product when introduced to it.

ii. The probability distribution that best describes this situation is the binomial distribution. This is because there are two possible outcomes for each person introduced to the product: they either buy it or they don't. The probability of buying the product is fixed at 60% for each person.

iii. To calculate the probability that exactly 9 people will buy the product, we can use the binomial probability formula:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

where n is the sample size, k is the number of successes, p is the probability of success, and (n choose k) is the number of ways to choose k successes from n trials. Plugging in the values, we get:

P(X=9) = (15 choose 9) * (0.6^9) * (0.4^6) = 5005 * 0.6^9 * 0.4^6 ≈ 0.1960, or approximately 19.60%