Exam 8: Continuous Probability Distributions

Suppose you have an F distribution with degrees of freedom 10, 20. a.Find the mean b.Find the variance. c.Find the standard deviation.

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

NARRBEGIN: Counter Sales 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.NARREND -{Counter Sales Narrative} Use the appropriate exponential distribution to find the probability that the next customer will not arrive within the next 2 minutes.

A national standardized testing company can tell you your relative standing on an exam without divulging the mean or the standard deviation of the exam scores.

P(Z > 3.00) is approximately ____________________.

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 exactly one hour to finish the test.

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.

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

What number corresponds to F_0.95,4,8?

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)

NARRBEGIN: Waiting Time 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.NARREND -{Waiting Time Narrative} What is the probability that a patient would have to wait between one and two hours?

The shape of the density function for an exponential distribution is ____________________.

NARRBEGIN: IT Graduates Salary 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.NARREND -{IT Graduates Salary Narrative} What is the probability of a new graduate receiving a salary between $45,000 and $50,000?

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} Find the time at which 50% of the customers will continue to hold?

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

If the value of Z is z = 99, that means you are at the 99^th percentile on the Z distribution.

In its standardized form, the normal distribution:

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

We define $F _ { A } , v _ { 1 } , v _ { 2 }$ as the value of the F with v₁ and v₂ degrees of freedom such that the area to its right under the F curve is A, while $F _ { 1 } - A _ { 1 } v _ { 1 } , v _ { 2 }$ is defined as the value such that the area to its left is A.

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