Question

Based on historical data, your manager believes that 33% 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?

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

Answer should be 4 decimal places.

Answer 1

Solution

Given that,

p = 0.33

1 - p = 1 - 0.33 = 0.67

n = 147

= p = 0.33

=  [p ( 1 - p ) / n] =   [(0.33 * 0.67) / 147] = 0.0388

P( < 0.28 )

= P[( - ) / < (0.28 - 0.33) / 0.0388]

= P(z < -1.2887)

Using z table,

= 0.0988