Use the appropriate normal distribution to approximate the resulting binomial distribution.
Jorge sells magazine subscriptions over the phone. He estimates that the probability of his making a sale with each attempt is .12. What is the probability of Jorge making more than 10 sales if he makes 80 calls?

A) The probability is 0.2709.
B) The probability is 0.3465.
C) The probability is 0.2599.
D) The probability is 0.2683.

Question

Use the appropriate normal distribution to approximate the resulting binomial distribution. ​
Jorge sells magazine subscriptions over the phone. He estimates that the probability of his making a sale with each attempt is .12. What is the probability of Jorge making more than 10 sales if he makes 80 calls?
​
A) The probability is 0.2709.
B) The probability is 0.3465.
C) The probability is 0.2599.
D) The probability is 0.2683.

Quizplus · Accepted Answer

To approximate the binomial distribution with a normal distribution, we use the mean (μ) and standard deviation (σ) of the binomial distribution. The mean is given by μ = np and the standard deviation by σ = sqrt(np(1-p)), where n is the number of trials (80 calls) and p is the probability of success (0.12). Thus, μ = 80 * 0.12 = 9.6 and σ = sqrt(80 * 0.12 * 0.88) ≈ 2.83. To find the probability of making more than 10 sales, we look for P(X > 10). We convert this to a z-score and use the normal distribution table or calculator. The calculation leads to the probability of approximately 0.2709, making option A correct.

Use the Appropriate Normal Distribution to Approximate the Resulting Binomial