Math Question #2

Question

Based on historical data, your manager believes that 33% of the company's orders come from first-time customers. A random sample of 76 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is less than 0.31?

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

Answer 1

population proportion (p) = 0.33

sample size (n) = 76)

want to find P(phat < 0.31)

transform inequality to standard normal (z):

z = (phat - p)/sqrt(p * (1-p)/n) = (0.31 - 0.33)/sqrt(0.33 * 0.67/76) = -0.37

P(phat < 0.31) = P(z < -0.37) = 0.3557