Question

A survey found that 25% of pet owners had their pets bathed professionally rather than doing it themselves. if 18 pet owners are randomly selected, the probability that exactly 5 people have their pets bathed professionally is ____________.

a) 18.88%
b) 18.99%
c) 19.88%
d) 21.99%

Answer 1

To find the probability that exactly 5 people have their pets bathed professionally out of a group of 18 pet owners, we can use the binomial probability formula. The probability is approximately 18.88%.

Step-by-step explanation:

To find the probability that exactly 5 people have their pets bathed professionally out of a group of 18 pet owners, we can use the binomial probability formula.

The formula is:

P(X=k) = C(n,k) * pk * (1-p)(n-k)

Where:

• P(X=k) is the probability of exactly k successes
• C(n,k) is the number of combinations of n items taken k at a time
• p is the probability of a single success
• n is the total number of trials

In this case, k=5, n=18, and p=0.25.

Plugging these values into the formula:

P(X=5) = C(18,5) * (0.25)5 * (1-0.25)(18-5) = 0.1888

Therefore, the probability that exactly 5 people have their pets bathed professionally is approximately 18.88%, which corresponds to option a).