Exam 6: Continuous Probability Distributions

For any normally distributed random variable with mean μ and standard deviation σ,the percent of the observations that fall between [μ - 2σ,μ + 2σ] is the closest to ______.

Compute the mean and variance of a lognormal variable Y if the mean and the variance of the underlying normal variable are

We are often interested in finding the probability that a continuous random variable assumes a particular value.

The waiting time at an elevator is uniformly distributed between 30 and 200 seconds.What is the probability a rider must wait between 1 minute and 1.5 minutes?

On average,a certain kind of kitchen appliance requires repairs once every four years.Assume that the times between repairs are exponentially distributed.Which of the following Excel commands computes the probability that the appliance will work no more than three years without requiring repairs?

The time to complete the construction of a soapbox derby car is normally distributed with a mean of three hours and a standard deviation of one hour.Find the probability that it would take more than five hours to construct a soapbox derby car.

On a particular busy section of the Garden State parkway in New Jersey,police use radar guns to detect speeding drivers.Assume the time that elapses between successive speeders is exponentially distributed with the mean of 15 minutes.What is the probability of a waiting time less than 10 minutes between successive speeders?

Just as in the case of the continuous uniform distribution,the probability density function of the normal distribution may be easily used to compute probabilities.

Let the lifetime of a new Jet Ski be represented by a lognormal variable, where X is normally distributed.Let the mean of the lifetime of the Jet Ski be six years with a standard deviation of three years. What proportion of the Jet Skis will last nine or more years?

You are planning a May camping trip to Denali National Park in Alaska and want to make sure your sleeping bag is warm enough.The average low temperature in the park for May follows a normal distribution with a mean of 32°F and a standard deviation of 8°F. One sleeping bag you are considering advertises that it is good for temperatures down to 25°F.What is the probability that this bag will be warm enough on a randomly selected May night at the park?

Patients scheduled to see their primary care physician at a particular hospital wait,on average,an additional eight minutes after their appointment is scheduled to start.Assume the time that patients wait is exponentially distributed. What is the probability a randomly selected patient will have to wait more than 10 minutes?

The time to complete the construction of a soapbox derby car is normally distributed with a mean of three hours and a standard deviation of one hour.Find the probability that it would take exactly 3.7 hours to construct a soapbox derby car.

Gold miners in Alaska have found,on average,12 ounces of gold per 1000 tons of dirt excavated with a standard deviation of 3 ounces.Assume the amount of gold found per 1000 tons of dirt is normally distributed. What is the probability the miners find more than 16 ounces of gold in the next 1000 tons of dirt excavated?

The cumulative distribution function is denoted and defined as which of the following?

Find the probability P(-1.96 ≤ Z ≤ 0).

How many parameters are needed to fully describe any normal distribution?

It is known that the length of a certain product X is normally distributed with $\mu$ = 20 inches.How is the probability related to ?

The normal probability distribution is symmetric and bell-shaped.

Suppose the round trip airfare between Boston and Orlando follows the normal probability distribution with a mean of $387.20 and a standard deviation of $68.50.What is the probability that a randomly selected airfare between Boston and San Francisco will be between $325 and $425?

Snack food companies always have a target weight when filling a box of snack crackers.It is not possible,however,to always fill boxes to the exact target weight.For a particular box of crackers,the target weight is 14 ounces.The filling machine drops between 13.5 and 15 ounces of crackers into each box.If these weights are uniformly distributed,what is the expected value of the fill weights? Does this value match the target weight? If not,what impact does this difference have on the manufacturer's costs to produce these crackers?