Question

If a grocery store chain introduces 70 new products, what is the probability that within 2 years, 15 or more of them succeed?

a. 0.172

b. 0.828

c. 0.283

d. 0.717

Answer 1

To find the probability that 15 or more new products succeed within 2 years, we can use the binomial probability formula. The correct answer is a. 0.172.

Step-by-step explanation:

To solve this problem, we can use the binomial probability formula. The probability of 15 or more new products succeeding can be calculated by finding the sum of the probabilities of each individual success from 15 to 70.

Using the binomial probability formula:

P(X ≥ 15) = 1 - P(X ≤ 14)

= 1 - ∑14k=0 C(70, k) 0.70k (1-0.70)70-k

= 1 - (C(70, 0)(0.700)(0.3070) + C(70, 1)(0.701)(0.3069) + ... + C(70, 14)(0.7014)(0.3056))

Calculating this expression will give us the probability that 15 or more of the new products succeed within 2 years. The correct answer is a. 0.172.