Exam 6: Continuous Probability Distributions

Suppose that the probabilities for intervals of time between successive occurrences of an event are described by an exponential distribution.The standard deviation of this distribution:

In the graph of a continuous uniform probability function, the height of the function is different for various values of x.

In a continuous probability distribution, area, not height, represents probability.

Smaller values of the standard deviation result in a normal curve that is wider and flatter.

During late-night hours, the 10^th Street convenience store averages four customers per hour.No customers have arrived in the last half-hour.Assuming that all Poisson conditions are met, determine the probability that it will be between 15 and 30 more minutes before the next customer arrives.

The search time for a particular search term on Google is defined by the probability density function below, where x = the random variable "time to produce a result in milliseconds".Determine the probability that the search will take no more than 253.5 milliseconds. 1/5 for values of x between 250 and 255 F(x) = 0 everywhere else

For a continuous random variable x, the probability density function f(x) represents:

North Dakota Mining (NDM) describes its estimate of the amount of oil it will produce next year from its western North Dakota operations with a normal distribution.The distribution is centered on 5.2 million barrels and has a standard deviation of .7 million barrels.According to this distribution, there is a .005 probability that NDM's production will be greater than how many millions of barrels?

The standard deviation of a normally distributed random variable:

When playing a round of golf, the distance of the drive off the second tee in feet is considered to be a continuous variable.

Incidents involving serious engine problems on the DD-340 aircraft are rare.They occur at an average rate of 3.0 per year (or .25 incidents per month).Assume all Poisson conditions are met.Use the exponential distribution to determine the probability that no incidents occur during the next 6 months.

For a continuous probability distribution, it is possible to talk about the probability of a random variable assuming a particular value, just like is done in a discrete probability distribution.

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 between 15000 and 18000 kwh?

During late-night hours, the 10^th Street convenience store averages four customers per hour.No customers have arrived in the last half-hour.Assuming that all Poisson conditions are met, determine the probability that the next customer arrives in less than 10 minutes.

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.What is the probability that an employee spends more than two hours reading and answering e-mail?

The speed of college tennis player Jaron Jackson's first serve averages 125 mph, with a standard deviation of 4 mph.If the distribution of service speeds is normal, what proportion of Jaron's serves will be between 120 and 130 mph?

North Dakota Mining (NDM) describes its estimate of the amount of oil it will produce next year from its western North Dakota operations with a normal distribution.The distribution is centered on 5.2 million barrels and has a standard deviation of .7 million barrels.According to this distribution, how likely is it that NDM's production will be less than 4.5 million barrels?

Shelton Products' website averages 4.0 visitors per minute.Visitor arrivals appear random and unrelated.(Assume all the Poisson conditions are met.) How likely is it that at least a minute will elapse before the next visitor arrives?

Births in the US occur at an average rate of 7.5 births per minute (Source: Census.gov, 2013).Assume all the Poisson conditions are met.What is the standard deviation (in minutes) of the "time between births" random variable?

Lionel receives an average of 3.0 text messages per minute.Assuming that all the Poisson conditions are met for the random variable "number of text message received in a minute," determine the standard deviation of the random variable "time between text messages" in seconds.