What is the probability that the sample proportion is greater than 0.26?

Question

Based on historical data, your manager believes that 27% of the company's orders come from first-time customers. A random sample of 56 orders will be used to estimate the proportion of first-time customers. What is the probability that the sample proportion is greater than 0.26?

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

Answer 1

going to use standardized normal statistic:

z = (phat - p) / sqrt(p * (1-p)/n)

where phat = 0.26, p = 0.27, n = 57

P(phat > 0.26) = P(z > (0.26 - 0.27)/sqrt(0.27*0.73/56) = P(z > -0.1686) = 1 - P(z < -0,1686) = 1 - 0.433 = 0.567