Exam 6: Continuous Probability Distributions

What proportion of values in a normal distribution will be in an interval that starts at 2.0 standard deviations to the left of (or below) the mean and extends to 1.0 standard deviation to the right of (or above) the mean?

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 131 and 133 mph?

Suppose that coffee sales at the Daily Grind are normally distributed with a mean of 225 cups sold each day and a standard deviation of 35 cups.Baristas at the Daily Grind receive a bonus if sales exceed 300 cups.What is the probability that the baristas will receive a bonus on any given day?

Kelso Motor Parts produces a car battery with a useful life that has a normal distribution.Average life is 40,000 miles, with a standard deviation of 1500 miles.What proportion of the batteries will have a useful life of less than 39,000 miles?

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 88,000 and 104,000 cubic feet are extracted?

JewelMist.com estimates the cost of relocating its headquarters to Los Gatos, CA with a normal distribution centered on $9.5 million and having a standard deviation of $1.1 million.According to this distribution, there's a 60% chance that costs will be less than how many millions of dollars.

For a continuous uniform probability density function, the height of the function decreases as x increases.

For a standard normal distribution, a negative value of z indicates:

For a standard normal distribution, find the area between z = -1.68 and z = +1.4.

Kelso Motor Parts produces a car battery with a useful life that has a normal distribution.Average life is 40,000 miles, with a standard deviation of 1500 miles.What proportion of the batteries will have a useful life between 42,000 and 44,000 miles?

Kelso Motor Parts produces a car battery with a useful life that has a normal distribution.Average life is 40,000 miles, with a standard deviation of 1500 miles.What proportion of the batteries will have a useful life of more than 43,000 miles?

Kelso Motor Parts produces a car battery with a useful life that has a normal distribution.Average life is 40,000 miles, with a standard deviation of 1500 miles.Suppose the company wants to establish a warranty policy.Any battery not lasting as long as the warranty mileage will be replaced free of charge.What warranty mileage would you suggest to ensure that the company won't have to replace more that 3% of the batteries sold?

JewelMist.com estimates the cost of relocating its headquarters to Los Gatos, CA with a normal distribution centered on $9.5 million and having a standard deviation of $1.1 million.JewelMist wants to budget for the move so that there's only a 1% chance that the actual cost will exceed the budgeted amount.JewelMist should budget how many millions of dollars.

Which of the following is NOT true of the normal probability distribution?

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, it is 68.3% likely that the amount extracted will be between 69,900 and how many cubic feet.

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 less than 136 mph?

Random variable x has a uniform distribution defined by the probability density function below.Determine the standard deviation of the random variable. 1/100 for values of x between 200 and 300 F(x) = 0 everywhere else

To determine probability using the standard normal distribution:

The search time for a particular search term on Google is defined by the probability density function below, where x = random variable "time to produce a result in milliseconds".Determine the standard deviation of x. 1/5 for values of x between 250 and 255 f(x) = 0 everywhere else

Suppose that a random variable Y is uniformly distributed between 50 and 100.What might Y represent?