Based on historical data, your manager believes that 41% of the company's orders come from first-time customers. A random sample of 72 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.35 and 0.5?

Answer:The probability that the sample proportion is between 0.35 and 0.5 is 0.7895Step-by-step explanation:To calculate the probability that the sample proportion is between 0.35 and 0.5 we need to know the z-scores of the sample proportions 0.35 and 0.5. z-score of the sample proportion is calculated as z=[tex]\frac{p(s)-p}{\sqrt{\frac{p*(1-p)}{N} } }[/tex] where p(s) is the sample proportion of first time customers p is the proportion of first time customers based on historical dataN is the sample sizeFor the sample proportion 0.35:z(0.35)=[tex]\frac{0,35-0.41}{\sqrt{\frac{0.41*0.59}{72} } }[/tex] ≈ -1.035For the sample proportion 0.5:z(0.5)=[tex]\frac{0,5-0.41}{\sqrt{\frac{0.41*0.59}{72} } }[/tex] ≈ 1.553The probabilities for z of being smaller than these z-scores are:P(z<z(0.35))= 0.1503 P(z<z(0.5))= 0.9398Then the probability that the sample proportion is between 0.35 and 0.5 is P(z(0.35)<z<z(0.5))= 0.9398 - 0.1503 =0.7895