Exam 8: Continuous Probability Distributions

If X has a normal distribution with mean 60 and standard deviation 6, which value of X corresponds with the value z = 1.96?

For a continuous random variable, the probability for each individual value of X is ____________________.

The Student t distribution with parameter v = 4 has a variance V(t) equal to:

Phone Orders The L.L.Bean catalog department that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product.The length of time was found to be a random variable best approximated by an exponential distribution with a mean equal to 3 minutes. -{Phone Orders Narrative} Find the time at which 50% of the customers will continue to hold?

Light Bulb Lifetime The lifetime of a light bulb (in hours) is exponentially distributed with $\lambda$ = 0.008. -{Light Bulb Lifetime Narrative} Find the probability that a light bulb will last between 120 and 140 hours.

Let X represent weekly income expressed in dollars.Since there is no set upper limit, we cannot identify (and thus cannot count) all the possible values.Consequently, weekly income is regarded as a continuous random variable.

A continuous probability distribution represents a random variable having an infinite number of outcomes which may assume any number of values within an interval.

As the ____________________ degrees of freedom increase, the mean of the F distribution approaches 1.

If P(t > t_.01,v) = 2.50, then the number of degrees of freedom v is:

To be a legitimate probability density function, all possible values of f(x) must be non-negative.

Diet Researchers studying the effects of a new diet found that the weight loss over a one-month period by those on the diet was normally distributed with a mean of 10 pounds and a standard deviation of 5 pounds. -{Diet Narrative} If a dieter is selected at random, what is the probability that the dieter lost more than 7.5 pounds?

The probability density function f(x) for a uniform random variable X defined over the interval [2, 10] is

Counter Sales Suppose that customers arrive at a counter at an average rate of three customers per minute and that their arrivals follow the Poisson model. -{Counter Sales Narrative} Use the appropriate exponential distribution to find the probability that the next customer will arrive within 1.5 minutes.

IT Graduates Salary The recent average starting salary for new college graduates in IT systems is $47,500.Assume salaries are normally distributed with a standard deviation of $4,500. -{IT Graduates Salary Narrative} What percent of starting salaries are no more than $42,250?

Use the F table to find the following probabilities. a. P(F_6,14 > 2.85) b. P(F_20,60 > 2.20) c. P(F_12,25 > 2.51) d. P(F_15,30 > 2.01)

Which of the following can have an exponential distribution?

A random variable X has a normal distribution with a mean of 250 and a standard deviation of 50.Given that X = 175, its corresponding value of Z is -1.50.

P(Z > 1.9) = ____________________ P(Z < 1.9).

Probability for continuous random variables is found by finding the ____________________ under a curve.

If X has an exponential distribution, the possible values of X are from ____________________ to infinity.