Respuesta :
Answer:
=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.
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
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
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:
- 70% of the customers in a sporting goods store purchase a pair of running shoes, hence [tex]p = 0.7[/tex]
- A random sample of 25 customers is selected, hence [tex]n = 25[/tex].
- Between 5 and 10 customers, hence [tex]a = 5, b = 10[/tex].
Then, the Excel statement is:
BINON.DIST.RANGE(25, 0.75, 5, 10)
For more on the binomial distribution, you can check https://brainly.com/question/24863377
