A recent survey found that 70% of all adults over 50 wear sunglasses for driving. In a random sample of 10adults over 50, what is the probability that at least six wear sunglasses?
A) 0.850
B) 0.700
C) 0.200
D) 0.006

Question

Quizplus · Accepted Answer

This problem can be solved using the binomial probability formula, which is P(X = k) = (nCk) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successful trials, p is the probability of success on a single trial, and nCk is the combination of n items taken k at a time. Here, n = 10, p = 0.70, and we're interested in the probability of at least 6 successes (k ≥ 6), which means we need to calculate the sum of probabilities for k = 6, 7, 8, 9, and 10. Instead of calculating each probability individually and summing them up, recognizing that this is a common type of problem, we can use statistical software or tables that have these cumulative probabilities pre-calculated. The result of this cumulative probability for at least 6 successes out of 10 with a success probability of 0.70 is approximately 0.850, indicating that there's an 85% chance that at least 6 out of 10 adults over 50 in a random sample will wear sunglasses for driving.

A Recent Survey Found That 70% of All Adults Over