Math Question #4

Question

Based on historical data, your manager believes that 42% of the company's orders come from first-time customers. A random sample of 165 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.31 and 0.47?

Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations.

Answer 1

phat = sample proportion

p = population proportion = 0.42

n = 165

Want to compute: P ( 0.31 < phat < 0.47)

Translate limits 0.31 and 0.47 to z, using equation: (phat - p)/sqrt(p * (1-p)/n)

for 0.31, we get z = (0.31 - 0.42)/sqrt(0.42 * 0.58/165) = -2.86

for 0.47, we get z = (0.47 - 0.42)/sqrt(0.42 * 0.58/165) = 1.3

so P(0.31 < phat < 0.47) = P(-2.86 < z < 1.3) = P(z < 1.3) - P(z < -2.86) = 0.9032 - 0.0021 = 0.9011