STAT 243 Portland Community College Sampling Distribution of a Proportion Problems

Based on historical data, your manager believes that 35% of the company’s orders come from first-time customers. A random sample of 102 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?

Based on historical data, your manager believes that 28% of the company’s orders come from first-time customers. A random sample of 111 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is greater than than 0.18?

Based on historical data, your manager believes that 36% of the company’s orders come from first-time customers. A random sample of 164 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.27 and 0.47?

According to a 2009 Reader’s Digest article, people throw away about 11% of what they buy at the grocery store. Assume this is the true proportion and you plan to randomly survey 98 grocery shoppers to investigate their behavior. What is the probability that the sample proportion does not exceed 0.15?

A Food Marketing Institute found that 31% of households spend more than $125 a week on groceries. Assume the population proportion is 0.31 and a simple random sample of 357 households is selected from the population. What is the probability that the sample proportion of households spending more than $125 a week is less than 0.32?