Focus groups of 12 people are randomly selected to discuss the Dixie name. It is determined that the mean number (per group) who think the name should be changed is 5.8, with a standard deviation of 1.22. Would it be unusual in one of these groups to find that 3 people think the name should be changed?

Annual customer demand for utensil sets has remained relatively steady for a long time, with an average of 5 million and a standard deviation of 350 thousand. Based on this information, and for a randomly selected year, answer the following questions. For what number of utensil sets (x) is the probability 70% that annual demand is less than that number? (round answer to 0 decimal) [x1] For what number of utensil sets (x) is the probability 52% that annual demand is greater than that number? (round answer to 0 decimal) [x2]

If z is a standard normal variable (normally distributed), find the probability that z is greater than 0.25. Probability = [probability] Note: answer in decimal form and round to 3 decimal places.

Are the following pairs of events Dependent or Independent? Event A: Some incites a riot. Event B: Someone gets hurt.

If z is a standard normal variable (normally distributed), find the probability that z lies between 0.70 and 1.98. Probability = [probability] Note: answer in decimal form and round to 3 decimal places.

If z is a standard normal variable (normally distributed), find the probability that z is less than 0.97. Probability = [probability] Note: answer in decimal form and round to 3 decimal places.

Data indicates that 48% of voters favor a certain ballot measure. For groups of 45 voters, find the variance. Hint: the distribution is binomial. Variance = [variance] Note: answer in decimal form and round to 2 decimal places

Willy Wonka claims that 75% of all Gobbstopper candy it produces weighs more than 0.5 ounces. Suppose that 800 Gobbstoppers are selected at random from the production line. What are the lower and upper limits of what would be considered a “usual” number that meets Willy’s claim? Lower limit of “usual” = [lower] Upper limit of “usual” = [upper] Note: answer in decimal form and round to 1 decimal place

What is the probability of an event that cannot occur? [probi] What is the probability of an event that is certain to occur? [probc] What is the best estimate of the probability of event about which you have no information? [probu]

Brian Head Ski Resort has a new quad (4 person) chairlift. A study of skiers shows the average weight among all skiers is 125 lbs, with a standard deviation of 30 lbs. Using the Central Limit Theorem, find the following probabilities for the mean weight of a randomly selected group of 4 skiers. What is the probability that the mean weight among a group of 4 skiers is less than 150 lbs? [p1] What is the probability that the mean weight among a group of 4 skiers is more than 130 lbs? [p2] Would it be unusual to find a mean weight of more than 130 lbs among 4 randomly selected skiers? (yes or no) [yesno] What is is the probability that the mean weight among a group of 4 skiers is between 120 and 130 lbs? [p3] Note: round all probabilities to 3 decimal places