Exam 6: Continuous Random Variables

A paint sprayer coats a metal surface with a layer of paint between 0.43 and 1.23 millimeters thick.The thickness of the coat of paint is approximately uniformly distributed. What is the standard deviation of the thickness of the coat of paint on the metal surface?

A continuous random variable may assume only integer values in a given interval.

The fill weight of a certain brand of adult cereal is normally distributed with a mean of 910 grams and a standard deviation of 5 grams. If we select one box of cereal at random from this population,what is the probability that it will weigh more than 904 grams?

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

The weight of a product is normally distributed with a standard deviation of .5 ounces.What should the average weight be if the production manager wants no more than 10% of the products to weigh more than 4.8 ounces?

The fill weight of a certain brand of adult cereal is normally distributed with a mean of 910 grams and a standard deviation of 5 grams. If we select one box of cereal at random from this population,what is the probability that it will weigh less than 900 grams?

While conducting experiments,a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m.What is the standard deviation of the water depth?

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. What is the probability that a sheet selected at random will be less than 31 inches long?

Suppose that the times required for a cable company to fix cable problems in its customers' homes are uniformly distributed between 40 minutes and 65 minutes. What is the probability that a randomly selected cable repair visit will take at least 50 minutes?

__________ values of the standard deviation results in a normal curve that is wider and flatter.

The cashier service time at the local branch of the Rivertown bank has an exponential distribution with a mean of 2.5 minutes.What is the probability that the service time: Exceeds 3 minutes?

A set of final examination grades in a calculus course was found to be normally distributed with a mean of 69 and a standard deviation of 9. What percentage of students scored between 81 and 89?

The life of a light bulb is exponentially distributed with a mean of 1,000 hours.What is the probability that the bulb will last: More than 1,200 hours?

A manufacturer of personal computers sets tests competing brands and finds that the amounts of energy they require are normally distributed with a mean of 285 kwh and a standard deviation of 9.1 kwh. If the lowest 25% and the highest 30% are not included in a second round of tests,what are the upper and lower limits for the energy amounts of the remaining sets?

Consider a normal population with a mean of 10 and a standard deviation 2. Find P(X < 12).

While conducting experiments,a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m.What is the probability that a randomly selected depth is less than 3.60 m?

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?

During the past six months,73.2% 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. Find the probability that a household spent more than $10.00

Consider a normal population with a mean of 10 and a variance of 4.Find P(X > 7).

If the random variable X has a mean of µ and a standard deviation $\sigma$ then (X - µ)/ $\sigma$ has a mean and standard deviation respectively: