Exam 6: Modeling Random Events: the Normal and Binomial Models

Some statisticians use a guideline that says that events that happen 5% of the time or less often should be considered "unusual." By this standard, is it unusual to have a car speed of 75 mi/hr or greater?

The distribution of gas consumption for SUVs driving on flat highways is approximately Normal with a center of 24.8 mpg and a standard deviation of 5 mpg. Which one of the following statements would explain a larger spread of the normal distribution?

A data set of gas consumption for trucks (in miles per gallon) is approximately normally distributed with a center of 24.8 mpg and a standard deviation of 5 mpg. Which one of the following statements would explain a smaller spread of the normal distribution?

Can the following problem be solved by using a binomial model? Let's say that the probability that a student will arrive on time for a statistics class is 70%. How many students out of 30 would be on time for the last day of class?

Use the following information to answer questions . A package delivery service divides their packages into weight classes. Suppose that the packages in the 14-20 pound class are uniformly distributed, meaning that all weights within that class are equally likely to occur. The probability density curve is shown below. -Find the probability that a randomly selected package will weigh less than 18 pounds.

Suppose that weights of cans of Benneke brand peaches have a population mean of 13.5 ounces and a population standard deviation of 0.33 ounces and are approximately normally distributed. Which of the following statements are correct? Choose the best statement.

The distribution of gas consumption for SUVs (in miles per gallon) is approximately normally distributed with a center of 24.8 mpg and a standard deviation of 5 mpg. A similar data set for a group of sedans is approximately normally distributed with a center of 28 mpg and a standard deviation of 4 mpg. Which one of the following statements is true when the distributions are compared on a number line?

Use the following information for following questions . The mean time it takes for workers at a factory to insert a delicate bolt into an engine is 15 minutes. The standard deviation of time to insert the bolt is 4.0 minutes and the distribution of time is approximately normally distributed. -97.5% of the time, the bolt is inserted in less than which time value? Round to the nearest whole number.

Use the following information to answer questions . Suppose that a binomial distribution is illustrated by the figure below, showing specific probabilities for each x value. -What is the approximate probability that x = 6 or less? Round to nearest hundredth place.

A summary of the types of movies showing in a small city, contains five genres. The following table shows the genres and the associated probability for that type of movie available on a particular weekend. The table is a probability distribution. If we chose a theater and movie to attend at random, what probability would we have of seeing anything other than a romantic or sci-fi movie?

Use the following information to answer questions . Suppose that a binomial distribution is illustrated by the figure below, showing specific probabilities for each x value. -What is the approximate probability that x = more than 10? Round to the nearest hundredth place.

Assume 80% of adults with arthritis symptoms report relief with a specific medication. If a new medication is given to 10 new patients with symptoms, what is the probability that the medication effectively relieves their symptoms? Select the most accurate statement to investigate the assumptions for using a binomial distribution model.

Determine whether the variable would best be modeled as continuous or discrete: The temperature of a cup of coffee dispensed from a beverage vending machine, taken four times during a 24-hour period.

Use the following information for following questions . The Normal distribution below models the distribution of highway gas consumption (in miles per gallon) for a large collection of SUVs when driving on level roads. The center is shown at 24.8 mpg and the standard deviations reflect the spread of the data. -What percent of SUVs consume 37.2 mpg or less?

Use the following information for following questions . Male players at the high school, college and professional ranks use a regulation basketball that weighs 22.0 ounces with a standard deviation of 1.0 ounce. Assume that the weights of basketballs are approximately normally distributed. -Roughly what percentage of regulation basketballs weigh more than 23.1 ounces? Round to the nearest tenth of a percent.

Use the following information to answer questions . -What is the approximate probability that x is equal to more than 10? Round to the nearest hundredth place.

Which of the following characteristics are not required for the binomial model?

Determine whether the variable would best be modeled as continuous or discrete: The number of tails when flipping ten coins.

Use the following information for following questions . Male players at the high school, college and professional ranks use a regulation basketball that weighs 22.0 ounces with a standard deviation of 1.0 ounce. Assume that the weights of basketballs are approximately normally distributed. -If a regulation basketball is randomly selected, what is the probability that it will weigh between 19.5 and 22.5 ounces? Round to the nearest thousandth.

Suppose that the probability that a person between the ages of 19 and 24 buys at least one tabloid magazine per week is 0.115. If 500 randomly selected people between the ages of 19 and 24 were asked "Do you buy at least one tabloid magazine per week?", would you be surprised if 45 or more said yes to this question? Why?