Exam 6: Continuous Probability Distributions

North Pacific Cannery (NPC) in British Columbia cans an average of 1250 cases of salmon daily, with a standard deviation of 40 cases.Assuming output has a normal distribution, on what proportion of days is NPC's output either less than 1180 cases or more than 1320 cases?

Suppose that the time that your employees spend reading and answering e-mail each day varies between 1.5 and 3.5 hours and is uniformly distributed over this range of values.Determine the standard deviation of the "time spent reading and answering e-mail" random variable.

The exponential probability density function produces a downward sloping curve that approaches the x axis as values of x gets larger.

A standard normal distribution is a normal distribution with a mean of and a standard deviation of .

The useful life (in years) of a shingled roof in Oregon has a uniform distribution described by the probability density function below.What is the standard deviation of the useful life distribution? 1/10 for values of x between 25 and 35 F(x) = 0 everywhere else

Approximately 99.7% of the values in a normal distribution will be within three standard deviations of the distribution mean.

The average (or expected) time it takes to complete a purchase at Trippler.com is 45 seconds.All the conditions for a Poisson distribution are met.Use the exponential distribution to determine the probability that it will take between 20 seconds and one minute to complete your next Trippler.com purchase.

Charanka Solar Park in India reports that it produces an average of 16,400 kilowatt hours (kwh) of electricity per day, with a standard deviation of 2200 kwh.If this electrical output has a normal distribution, for what proportion of days would we expect the day's output to be less than 12000 kwh?

For a normal distribution, find the area between the mean and a point 2.33 standard deviations to the right of the mean.

For a random variable x, the probability density function f(x) represents the height of the function at x.

The average fee per student (an amount that includes activities fees, technology fees, curriculum fees, etc.) at four-year colleges is $1043.The fee are normally distributed with a standard deviation of $68.If a student budgets $1075 for fees, how likely is it that he/she will end up at least $50 short?

Over a number of years, the average annual rate of return for Fidelity's Blue Chip Value mutual fund has been .08 with a standard deviation of .04.Assume annual returns are approximately normally distributed around the average rate.Using this historical information as the basis for your calculations, what is the probability of loss over the next year if you put money into this fund?

The useful life (in years) of a shingled roof in Oregon has a uniform distribution described by the probability density function below.What proportion of roofs have a useful life greater than 29 years? 1/10 for values of x between 25 and 35 F(x) = 0 everywhere else

A standard normal distribution is a normal distribution with:

Suppose that the high temperature on an August day in Death Valley varies between 98 and 118 degrees Fahrenheit and is uniformly distributed over this range of values.What is the probability that the high temperature will exceed 100 degrees on an August day?

The speed of college tennis player Jaron Jackson's first serve averages 125 mph, with a standard deviation of 4 mph.The distribution of service speeds is normal.Jaron's opponent today is certain that he can return for a winner any serve that is less than 116 mph.If this is true, what proportion of Jaron's serves will his opponent be sure to return for a winner?

In a recent year, the average marathon time for women in the US was 5 hours and 6 minutes (Source: Marathonguide.com).Suppose that marathon times are normally distributed around this average with a standard deviation of 50 minutes.What marathon time must a woman achieve in order to be among the fastest 10% of marathon runners?

At Netflix, the time it takes for a returned DVD to be re-filed and for the next DVD to be submitted for shipping to the customer follows a bell-shaped pattern, with a mean of 194 seconds and a standard deviation of 42 seconds.What proportion of the "turnaround" times are longer 180 seconds?

The average (or expected) time it takes to complete a purchase at Trippler.com is 45 seconds.All the conditions for a Poisson distribution are met.Use the exponential distribution to determine the probability that it will take less than 30 seconds to complete your next Trippler.com purchase.

A random variable that has a normal distribution with a mean of zero and a standard deviation of one is said to have a standard normal probability distribution.