Final answer:
The probability that at least six out of ten randomly selected customers want the oversize version of a tennis racket is 0.63145608.
Step-by-step explanation:
To find the probability that at least six out of ten randomly selected customers want the oversize version of a tennis racket, we can use the binomial probability formula. The binomial probability formula is P(X=k) = C(n, k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, p is the probability of success, and C(n, k) is the number of combinations of n items taken k at a time. In this case, n = 10, k can be any value from 6 to 10, p = 0.6, and q = 1 - p = 0.4.
To find the probability that at least six want the oversize version, we need to calculate the probabilities for k=6, 7, 8, 9, and 10, and add them together.
P(X=6) = C(10, 6) * (0.6)^6 * (0.4)^(10-6) = 0.250822656
P(X=7) = C(10, 7) * (0.6)^7 * (0.4)^(10-7) = 0.214990848
P(X=8) = C(10, 8) * (0.6)^8 * (0.4)^(10-8) = 0.120932351
P(X=9) = C(10, 9) * (0.6)^9 * (0.4)^(10-9) = 0.038654608
P(X=10) = C(10, 10) * (0.6)^10 * (0.4)^(10-10) = 0.0060466176
Adding these probabilities gives us:
P(X>=6) = P(X=6) + P(X=7) + P(X=8) + P(X=9) + P(X=10) = 0.63145608