A survey found that 25% of pet owners had their pets bathed professionally rather than doing it themselves. If 20 pet owners are randomly selected find the probability that between 12 and 7 pet owners, inclusive, have their pets bathed professionally.
Try the binomial probability function. If you have access to a binomial probability table, this will make the problem much easier to solve.
In most tables, you need to find x, n, and p. You will need to find each x value, then add together for your total probability. x = 7, 8, 9, 10, 11, 12. n = 20 and p = .25 for your other values.
I hope this will help.
To find the probability that between 12 and 7 pet owners, inclusive, have their pets bathed professionally when 20 pet owners are randomly selected, we need to calculate the probability of each scenario (12, 13, 14, 15, 16, 17) and then add them together.
The probability of exactly x pet owners out of 20 having their pets bathed professionally can be calculated using the binomial probability formula:
P(x) = (nCx) * (p^x) * ((1-p)^(n-x))
Where:
- P(x) is the probability of getting exactly x successes (pet owners who had their pets bathed professionally).
- n is the total number of trials (number of pet owners selected, which is 20 in this case).
- x is the number of successes (number of pet owners who had their pets bathed professionally, ranging from 12 to 17).
- p is the probability of a single success (probability of a pet owner having their pet bathed professionally, which is 0.25 in this case).
- (nCx) is the combination formula, calculated as n! / (x! * (n-x)!).
Now, let's calculate the probability for each scenario and sum them up:
P(12) = (20C12) * (0.25^12) * ((1-0.25)^(20-12))
P(13) = (20C13) * (0.25^13) * ((1-0.25)^(20-13))
P(14) = (20C14) * (0.25^14) * ((1-0.25)^(20-14))
P(15) = (20C15) * (0.25^15) * ((1-0.25)^(20-15))
P(16) = (20C16) * (0.25^16) * ((1-0.25)^(20-16))
P(17) = (20C17) * (0.25^17) * ((1-0.25)^(20-17))
Finally, sum up all these probabilities to get the desired result:
P(between 12 and 7) = P(12) + P(13) + P(14) + P(15) + P(16) + P(17)