Exam 6: Continuous Random Variables

Given that the length an athlete throws a hammer is a normal random variable with mean 50 feet and standard deviation 5 feet,what is the probability he throws it between 50 feet and 60 feet?

Consider a normal population with a mean of 10 and a variance of 4.Find P(X > 18).

A plant manager knows that the number of boxes of supplies received weekly is normally distributed with a mean of 200 and a standard deviation of 20.What percentage of the time will the number of boxes received weekly be between 180 and 210?

The average time a subscriber spends reading the local newspaper is 49 minutes.Assume the standard deviation is 16 minutes and that the times are normally distributed.What is the probability a subscriber will spend no more than 30 minutes reading the paper?

If x is a binomial random variable where n = 100 and p = .1,find the probability that x is less than or equal to 10,using the normal approximation to the binomial.

If the random variable of x is normally distributed,_____ percent of all possible observed values of x will be within two standard deviations of the mean.

The _____________ distribution would most likely be used to describe the distribution of time between arrivals of customers at the grocery store.

During the past six months,73.2 percent of US households purchased sugar.Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10.99 percent of the households spent less than what amount?

All continuous random variables are normally distributed.

The actual weight of hamburger patties is an example of a continuous random variable.

If the random variable x is normally distributed,______ percent of all possible observed values of x will be within three standard deviations of the mean.

An apple juice producer buys all his apples from a conglomerate of apple growers in one northwestern state.The amount of juice squeezed from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce.77 percent of the apples will contain at least how many ounces of juice?

The grade a student received on an examination was transformed to a z value,which was negative.Therefore,we know that he scored:

The weight of a product is normally distributed with a mean of four ounces and a variance of .25 squared ounces.What is the probability that a randomly selected unit from a recently manufactured batch weighs no more than 3.5 ounces?

Suppose that the waiting time for a license plate renewal at a local office of a state motor vehicle department has been found to be normally distributed with a mean of 30 minutes and a standard deviation of 8 minutes.Suppose that in an effort to provide better service to the public,the director of the local office is permitted to provide discounts to those individuals whose waiting time exceeds a predetermined time.The director decides that 15 percent of the customers should receive this discount.What are the numbers of minutes they need to wait to receive the discount?

The probability that an appliance is currently being repaired is .5.If an apartment complex has 100 such appliances,what is the probability that at least 60 are currently being repaired? Use the normal approximation to the binomial.

If the random variable x is normally distributed,68.26 percent of all possible observed values of x will be within two standard deviations of the mean.

The mean of a standard normal distribution is always equal to 1.

Suppose that the times required for a cable company to fix cable problems in the homes of its customers are uniformly distributed between 40 minutes and 65 minutes.What is the probability that a randomly selected cable repair visit falls within 2 standard deviations of the mean?

A property of continuous distributions is that: