# What is the probability that a sheet selected at random will be less than 29.75 inches long?

**Question 1: **The population of lengths of aluminum coated steal sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.2 inches. What is the probability that a sheet selected at random will be less than 29.75 inches long?

**Question 2: **The population of lengths of aluminum coated steal sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.2 inches. What is the probability that a sheet selected at random from the population is between 29.75 and 30.5 inches long?

**Question 3: **During the past six months, 73.2 % of US households purchase sugar. Assume that these expenditures are approximately normally distributed with a mean of $ 8.22 and a standard deviation of $ 1.10. find a probability that a household spend less than $ 5.0

**Question 4: **During the past six months, 73.2 % of US households purchase sugar. Assume that these expenditures are approximately normally distributed with a mean of $ 8.22 and a standard deviation of $ 1.10. What proportion of households spend between $ 5.0 and $ 9.

**Question 5: **The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.2 inches. A sample of four metal sheets is randomly selected from a batch. What is the probability that the average length of a sheet is between 30.25 and 30.35 inches long?

**Question 6: **The chief chemist of a major oil/gasoline production company claims that the regular unleaded gasoline produced by the company contains on average four ounces of certain ingredient. The chemist further states that the distribution of this ingredient per gallon of regular unleaded gasoline is normal and has a standard deviation of 1.2 ounces. What is the probability of finding an average in excess of 4.3 ounces of this ingredient from randomly inspected 100 gallons of regular unleaded gasoline?

**Question 7: **In the upcoming governor’s election, the most recent poll based on 900 respondents predicts that the incumbent will be reelected with55 % of the votes. For the sake of argument, assume that 51% of actual voters in the state support the incumbent governor (p=0.51). calculate the probability of observing a sample proportion of voters 0.55 or higher supporting the incumbent governor.

**Question 8: **according to hospital administrator, historical records over the past ten years have shown that 20 % of major surgery patients are dissatisfied with after-surgery care in the hospital. A scientific poll based on 400 hospital patients has just been conducted.

What is the probability that less than 64 patients will not be satisfied with the after surgery care.