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The probability that exactly 7 are men out of 10 sports car owners who are randomly selected is 0.215 given that 60% of people who purchase sports cars are men. This can be obtained by using binomial distribution formula.
Calculate the required probability:
This question can be solved using binomial distribution formula.
The formula for binomial distribution is the following,
P(X) = ⁿCₓ pˣ qⁿ⁻ˣ
where,
n = number of trials(or the number being sampled)
x = number of success desired
p = probability of getting a success in one trial
q = 1 - p = probability of getting a failure in one trial
Here in the question it is given that,
⇒ 60% of people who purchase sports cars are men
This statements clearly means that probability of men purchase sports cars is 60%.
⇒ P(men purchasers) = p = 60% = 0.6
From this we can find the probability of women who purchase sports cars,
⇒ P(women purchasers) = q = 1 - p = 1 - 0.6 = 0.4
So we can find the probability that exactly 7 are men out of 10 sports car owners who are randomly selected
It is a binomial case with n = 10
By using the formula for binomial distribution we get,
P(X = 7) = ¹⁰C₇ × 0.6⁷ × 0.4³
P(X = 7) = 120 × 0.0279936 × 0.064
P(X = 7) = 0.21499
P(X = 7) = 0.215
Hence the probability that exactly 7 are men out of 10 sports car owners who are randomly selected is 0.215 given that 60% of people who purchase sports cars are men.
Learn more about binomial distribution here:
brainly.com/question/13634543
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