Final answer:
To determine the probability that between 10 and 17 toasters require repairs, use the binomial probability formula. To determine the probability that less than 20 toasters require repairs, use the cumulative probability formula.
Step-by-step explanation:
To determine the probability that between 10 and 17 (exclusive) toasters will require repairs within the first 90 days after they are sold, we need to use the binomial probability formula. The formula is:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Where:
- P(X = k) is the probability that exactly k toasters require repairs
- n is the total number of toasters (200 in this case)
- k is the number of toasters that require repairs (between 10 and 17)
- p is the probability of a toaster requiring repairs (0.075 or 7.5%)
- C(n, k) is the number of combinations of n items taken k at a time
We can calculate the probabilities for each value of k between 10 and 17 and sum them up to get the total probability.
To determine the probability that less than 20 toasters will require repairs, we can use the cumulative probability formula:
P(X < k) = P(X = 0) + P(X = 1) + ... + P(X = (k-1))
We can calculate the probabilities for each value of k less than 20 and sum them up to get the total probability.