Respuesta :
The probability that more than 60 clients in the sample would answer yes to the survey question is 0.97.
What is probability?
It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
The question is incomplete.
The complete question is:
The big smiles portrait studio is conducting a survey among their clients. one of the questions being asked is if they would recommend the studio to a friend. the studio has given the survey to a simple random sample of 65 clients during the past 2 weeks. If the true proportion of clients who are very satisfied with the Big smiles Portrait studio and would therefore recommend it to a friend is 82%, what is the probability that more than 60 clients in the sample would answer yes to the survey question?
Let's suppose:
X(i) = {1; if person is unemployed}
0; otherwise
P[x(i) = 1] = p = 0.13
P[x(i) = 0] = 1 - p = 0.87
Now,
X = ∑(i = 1 to 6) = No of people unemployed.
Applying binomial theorem:
P[X = x] = C(6, x)(0.13)ˣ(0.87)⁶⁻ˣ; x = 0, 1, 2, 3...6
The probability:
P[X<3] = P(X = 0) + P(x = 1) + P(X = 2)
= C(6, 0)(0.13)⁰(0.87)⁶⁻⁰ + C(6, 1)(0.13)¹(0.87)⁶⁻¹ + C(6, 2)(0.13)²(0.87)⁶⁻²
After solving:
P[X<3] = 0.97
Thus, the probability that more than 60 clients in the sample would answer yes to the survey question is 0.97.
Learn more about the probability here:
brainly.com/question/11234923
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