Exam 6: Continuous Probability Distributions

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 at least 6 months will elapse before the incident.

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 won't arrive for at least 45 more minutes.

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, on 80% of the days, we would expect the day's output to be between 13,580 kwh and how many kwh.

The average fee per student (an amount that includes activities fees, technology fees, curriculum fees, etc.) at four-year colleges is $1043.The fee charges are normally distributed with a standard deviation of $68.What proportion of students pay fees between $950 and $1050?

A study reported by the Michigan State campus newspaper stated that the average time MSU students spent studying last month was is 58.3 hours, with a standard deviation of 14 hours.Assume the study time distribution is normal.According to study results, about 20% of MSU students spent less than how many hours last month studying.

What proportion of values in a normal distribution will be in an interval that starts at 2.58 standard deviations to the left of (or below) the mean and ends at 1.96 standard deviations to the left of (or below) the mean?

The amount of natural gas that Taylor Exploration extracts daily at its Cane Creek site in Utah has a normal distribution, with an average of 82,300 cubic feet and a standard deviation of 12,400 cubic feet.On a randomly selected day, how likely is it that between 75,000 and 90,000 cubic feet are extracted?

A study reported by the Michigan State campus newspaper stated that the average time MSU students spent studying last month was is 58.3 hours, with a standard deviation of 14 hours.If the study time distribution is normal, what percentage of students spent between 40 and 80 hours studying?

The waiting time before a caller is able to speak to a customer service representative at Chase Bank is exponentially distributed, with an average waiting time of 2.5 minutes.How likely is it that a caller will wait less than 2 minutes?

Dallas Green Homes uses a normal curve to estimate next year's demand.The distribution has a mean of 163 units and a standard deviation of 36 units.According to this demand distribution, how likely is it that demand will be between 180 and 240 units?

For a standard normal distribution, find the area between z = +1.36 and z = + 2.22.

One of the interesting properties of the exponential distribution is its lack of memory.

A study reported by the Michigan State campus newspaper stated that the average time MSU students spent studying last month was is 58.3 hours, with a standard deviation of 14 hours.If the study time distribution is normal, what percentage of students spent more than 70 hours studying?

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 mean (expected value) of x. 1/5 for values of x between 250 and 255 f(x) = 0 everywhere else

The speed of college tennis player Jaron Jackson's first serve averages 125 mph, with a standard deviation of 4 mph.The distribution of Jaron's serve speed is normal.Jaron's opponent today figures he can handle a serve speed up to 132 mph.If this is the case, what proportion of Jaron's serves will his opponent not be able to handle?

Dallas Green Homes uses a normal curve to estimate next year's demand.The distribution has a mean of 163 units and a standard deviation of 36 units.According to this demand distribution, there's a 5% chance that demand will be no more than how many units.

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 we would expect that on 95% of the days, the day's output would be between 12,090 kwh and how many kwh.

What proportion of values in a normal distribution will be between the mean and a point 1.75 standard deviations to the right of (or above) the mean?

Which of the following best describes the memoryless nature of the exponential distribution?

The waiting time before a caller is able to speak to a customer service representative at Chase Bank is exponentially distributed, with an average waiting time of 2.5 minutes How likely is it that a customer will wait at least 3 minutes?