A recent market study has determined that the probability that a young adult will be willing to try a new online financial service that your company is offering is 50%.In a random sample of 10 young adults,the approximate probability that at least 2 but no more than 3 will be willing to try this new service is _________.
A) 0.1575
B) 0.1612
C) 0.1775
D) 0.1812
E) 0.1975

Question

Quizplus · Accepted Answer

The probability of at least 2 but no more than 3 young adults being willing to try the new service can be calculated using the binomial distribution. The probability of exactly 2 young adults being willing to try the service is given by:P(X = 2) = (10 choose 2) * (0.5)^2 * (0.5)^8 = 0.1094The probability of exactly 3 young adults being willing to try the service is given by:P(X = 3) = (10 choose 3) * (0.5)^3 * (0.5)^7 = 0.0488Therefore, the approximate probability of at least 2 but no more than 3 young adults being willing to try the new service is:P(2 ≤ X ≤ 3) = P(X = 2) + P(X = 3) = 0.1094 + 0.0488 = 0.1582The closest answer choice to 0.1582 is A) 0.1575.

A Recent Market Study Has Determined That the Probability That