Exam 8: Continuous Probability Distributions

A worker earns $16 per hour at a plant and is told that only 5% of all workers make a higher wage.If the wage is assumed to be normally distributed and the standard deviation of wage rates is $5 per hour, find the average wage for the plant workers per hour.

A random variable with density function eS1^-x for x $\ge$ 0 has an exponential distribution with $\lambda$ = ____________________.

The exponential density function f(x):

In the exponential distribution, X takes on an infinite number of possible values in the given range.

If X has an exponential distribution, then f(x) approaches ____________________ as x approaches infinity.

Repair Time The time it takes a technician to fix a telephone problem is exponentially distributed with a mean of 15 minutes. -{Repair Time Narrative} What is the probability that it will take a technician less than 10 minutes to fix a telephone problem?

Calculus Scores Scores of high school students on a national calculus exam were normally distributed with a mean of 86 and a standard deviation of 4.(Total possible points = 100.) -{Calculus Scores Narrative} What is the probability that a randomly selected student will have a score of 80 or higher?

Use the t-table to find the following values of t. a. t_.10,9 b. t_.10,20 c. t_.025,82 d. t_.05,196

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 is the probability of a new graduate getting a starting salary in excess of $55,000?

Waiting Time The length of time patients must wait to see a doctor at an emergency room in a large hospital has a uniform distribution between 40 minutes and 3 hours. -{Waiting Time Narrative} What is the probability density function for this uniform distribution?

Let X be an exponential random variable with $\lambda$ = 1.50.Find the following: a. P(X $\ge$ 2) b. P(X $\le$ 4) c. P(1 $\le$ X $\le$ 3) d. P(X = 1)

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} What proportion of the dieters lost more than 12 pounds?

If the random variable X is exponentially distributed with parameter $\lambda$ = 0.05, then the probability P(X < 5) = .2865.

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} What proportion of callers are put on hold longer than 3 minutes?

If the random variable X is exponentially distributed and the parameter of the distribution $\lambda$ = 4, then P(X $\le$ 1) = 0.25.

You can use a continuous random variable to ____________________ a discrete random variable that takes on a countable, but very large, number of possible values.

Electronics Test The time it takes a student to finish a electronics test has a uniform distribution between 50 and 70 minutes. -{Electronics Test Narrative} What is the mean amount of time it takes a student to finish the test?

The variance of a Student t random variable with v degrees of freedom (v > 2) is always greater than 1.

If Z is a standard normal random variable, find the value z for which: a. the area between 0 and z is 0.3729 b. the area to the right of z is 0.7123 c. the area to the left of z is 0.1736 d. the area between-z and z is 0.6630

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} What proportion of customers having to hold more than 1.5 minutes will hang up before placing an order?