Final answer:
To calculate the probability that no more than 1 of the next 8 purchases will be returned, we can use the binomial probability formula. The probability is approximately 0.4243.
Step-by-step explanation:
To calculate the probability that no more than 1 of the next 8 purchases will be returned, we can use the binomial probability formula. The formula is:
P(X ≤ k) = C(n, 0) * p^0 * (1 - p)^(n - 0) + C(n, 1) * p^1 * (1 - p)^(n - 1)
Where:
- P(X ≤ k) is the probability of getting no more than k successes
- C(n, k) is the combination formula (n choose k)
- n is the number of trials
- p is the probability of success
In this case, n = 8, p = 0.06 (probability of a tall purchase being returned), and k = 1. Plugging these values into the formula gives:
P(X ≤ 1) = C(8, 0) * 0.06^0 * (1 - 0.06)^(8 - 0) + C(8, 1) * 0.06^1 * (1 - 0.06)^(8 - 1)
Calculating the values gives:
P(X ≤ 1) = 0.4243
Therefore, the probability that no more than 1 of the next 8 purchases will be returned is approximately 0.4243.