The manager of a retail store knows that 40% of the customers who enter the store will purchase one or more items and 60% will leave without making a purchase.what is the probability that in a sample of 10 customers,five will buy one or more items? Here,the population consists of both purchaser and non-purchaser customers.for a sample of 10 customers,find the probability that five will purchase one or more items.How does the sample result look like compared with the population parameter given?

Question

The manager of a retail store knows that 40% of the customers who enter the store will purchase one or more items and 60% will leave without making a purchase.what is the probability that in a sample of 10 customers,five will buy one or more items? Here,the population consists of both purchaser and non-purchaser customers.for a sample of 10 customers,find the probability that five will purchase one or more items.How does the sample result look like compared with the population parameter given?

(inferential statistics)

Answer 1

prob(buy) = .4

prob(not buy) = .6

prob(5 of 10 will buy)
= C(10,5) (.4)^5 (.6)^5
= 252(.000796..)
= appr .2007

Answer 2

To find the probability that exactly five customers out of a sample of 10 will purchase one or more items, we can use the binomial probability formula. The formula is:

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

Where:
- P(X = k) represents the probability of exactly k successes (customers purchasing) out of n trials (customers in the sample).
- (n choose k) represents the binomial coefficient, which calculates the number of ways to choose k items out of n.
- p is the probability of success on a single trial (probability of a customer purchasing).
- (1-p) represents the probability of failure on a single trial (probability of a customer not purchasing).

In this case, n = 10 (sample size) and p = 0.4 (probability of a customer purchasing). So, we need to calculate P(X = 5).

P(X = 5) = (10 choose 5) * (0.4^5) * (0.6^5)

Using a binomial calculator or a statistical software, we can find the result. The probability is approximately 0.200.

In terms of the sample result compared to the population parameter, the sample probability represents an estimate of the population parameter. The population parameter in this case is the proportion of customers who purchase items in the entire population of the retail store (which is 40%). When we take a sample of 10 customers, the probability of exactly five customers purchasing represents our estimate for the proportion of purchasers in the larger population. This estimate may be close to or different from the actual population parameter, depending on sampling variability. Using inferential statistics, we can obtain an interval estimate (confidence interval) to provide a range of values within which we can be reasonably confident the population parameter lies.