Question

A maker of greeting cards has an ink problem that causes the ink to smear on 7% of the cards. The daily production run is 500 cards. What is the probability that if a sample of 35 cards is checked, there will be ink smeared on at most 5 cards?

a) 0.0808

b) 0.0790

c) 0.8925

d) 0.9192

Answer 1

To find the probability of at most 5 cards with ink smeared in a sample of 35 cards, we can use the binomial probability formula. The probability is approximately 0.0790.

Step-by-step explanation:

To solve this problem, we can use the binomial probability formula. The probability of having ink smeared on a card is 7%, which means the probability of not having ink smeared on a card is 93%. The sample size is 35 cards, and we want to find the probability of having at most 5 cards with ink smeared.

The formula for the probability of at most k successes in n trials is:

P(X <= k) = ∑(x=0 to k) (nCx * px * qn-x)

Using this formula, we can calculate the probability of at most 5 cards:

P(X <= 5) = ∑(x=0 to 5) (35Cx * 0.07x * 0.9335-x)

Calculating this sum, we find that the probability is approximately 0.0790. So, the correct answer is (b) 0.0790.