Probabilty porportion question

Question

Based on historical data, your manager believes that 30% of the company's orders come from first-time customers. A random sample of 147 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is less than 0.28?

Answer 1

.28 * 147 = 41.16

The sample percentage is less than 28% if x <= 41

Thus, the exact answer can be found in Excel using P(x <= 41) = binom.dist(41,147,.3,1) =

.3234.

The normal approximation to this is found using the sample mean .3 and sample standard deviation

√(p(1-p)/n) = √(.3*.7/147) = .037796

Then, P(x <= .28) = P(z <= (.28-.3)/.037796) = P(z <= -.52915) = in Excel, normsdist(-.52915) =

.2984