A software developer makes 175 phone calls to its current customers. There is an 8 percent chance of reaching a given customer (instead of a busy signal, no answer, or answering machine). The normal approximation of the probability of reaching at least 20 customers is:
A).022.
B).007.
C).063.
D).937.

Question

Quizplus · Accepted Answer

First, we calculate the expected number of customers reached:
Expected value = 175 calls * 0.08 = 14 customers

Next, we calculate the standard deviation:
Standard deviation = sqrt(175 calls * 0.08 * (1-0.08)) = 2.76

Now, we need to standardize the value of 20 customers:
z = (x - mu) / sigma
z = (20 - 14) / 2.76 
z = 2.17

Using a standard normal distribution table or calculator, we find the probability of Z being greater than or equal to 2.17 to be 0.015. However, since we are dealing with proportions, we must use a correction factor:
Correction factor = 0.5 - (0.5 * erf(-2.17 / sqrt(2))) 
Correction factor = 0.049

Finally, we calculate the final probability using the correction factor:
P(X >= 20) = P(Z >= 2.17) - Correction factor
P(X >= 20) = 0.015 - 0.049
P(X >= 20) = 0.063

Therefore, the normal approximation of the probability of reaching at least 20 customers is 0.063 or choice C.

A Software Developer Makes 175 Phone Calls to Its Current