Exam 8: Continuous Probability Distributions

NARRBEGIN: ElectronicsTest Electronics Test The time it takes a student to finish a electronics test has a uniform distribution between 50 and 70 minutes.NARREND -{Electronics Test Narrative} Find the probability that a student will take more than 60 minutes to finish the test.

The variance of a $\chi$ ² distribution is twice the value of its mean.

A continuous random variable is one that can assume an uncountable number of values.

Tanner took a statistics test whose mean was 80 and standard deviation was 5. The total points possible was 100. Tanner's score was 2 standard deviations below the mean. What was Tanner's score, rounded to the nearest whole number?

The exponential distribution is suitable to model the length of time that elapses before the first telephone call is received by a switchboard.

NARRBEGIN: Phone Orders 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.NARREND -{Phone Orders Narrative} What is the probability that a randomly selected caller is placed on hold for 3 to 6 minutes?

NARRBEGIN: Diet 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.NARREND -If Z is a standard normal random variable, find the following probabilities: a.P(Z $\le$ -1.77) b.P(Z $\ge$ -1.96) c.P(0.35 $\le$ Z $\le$ 0.85) d.P(-2.88 $\le$ Z $\le$ -2.15) e.P(Z $\le$ 1.45)

The Student t distribution:

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

The variance of a Student t distribution approaches ____________________ as the degrees of freedom increase to infinity.

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

If the random variable X is exponentially distributed with parameter $\lambda$ = 1.5, then the probability P(2 $\le$ X $\le$ 4), up to 4 decimal places, is

The mean and the variance of an exponential distribution are equal to each other.

NARRBEGIN: Diet 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.NARREND -{Diet Narrative} What proportion of the dieters gained weight?

What proportion of the data from a normal distribution is within two standard deviations from the mean?

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.

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

What number corresponds to $x _ { 0.05,12 } ^ { 2 }$ ?

NARRBEGIN: Light Bulb Lifetime Light Bulb Lifetime The lifetime of a light bulb (in hours) is exponentially distributed with $\lambda$ = 0.008.NARREND -{Light Bulb Lifetime Narrative} What is the mean and standard deviation of the light bulb's lifetime?

If a point y lies outside the range of the possible values of a random variable X, then f(y) must equal zero.