It is known that 70% of the customers in a sporting goods store purchase a pair of running shoes. A random sample of 25 customers is selected. Assume that the customers’ purchases are made independently. In this binomial distribution application, which Excel statement will find the probability of between 5 and 10 customers, inclusively, purchasing a pair of running shoes?

Using the binomial distribution, it is found that the Excel statement that will find the probability of between 5 and 10 customers is:

BINON.DIST.RANGE(25, 0.75, 5, 10)

For each customer, there are only two possible outcomes, either they purchase a pair of running shoes, or they do not. Customers' purchases are independent, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

The parameters are:

Using Excel, the probability of the number of successes being between a and b, inclusive, is given by:

BINOM.DIST.RANGE(n, p, a, b)

In this problem:

Then, the Excel statement is:

BINON.DIST.RANGE(25, 0.75, 5, 10)

For more on the binomial distribution, you can check link

=BINOMDIST(10,25,70%,FALSE) -BINOMDIST(5,25,70%,FALSE)

0.001324586

Step-by-step explanation:

The success probability is p = 70% = 0.70

The number of trials are n = 25

The Excel formula for the binomial distribution is given by

BINOMDIST(Number_s, Trial_s, Probability_s, Cumulative)

Where

Numbers = 5 and 10

Trials = 25

Probability = 70%

Cumulative = FALSE

The probability of between 5 and 10 customers is then

=BINOMDIST(10,25,70%,FALSE) -BINOMDIST(5,25,70%,FALSE)

0.001324586

Note: FALSE option provides the probability of exactly 10 and 5 where TRUE option gives cumulative results (0 to 5 or 0 to 10) that would be wrong in this case.

p> q if you calculate p is100 q is 79