Questions from Applied Statistics

Q: The life of a recirculating pump follows a Weibull distribution with parameters

The life of a recirculating pump follows a Weibull distribution with parameters β = 2 and δ = 700 hours. Determine for parts (a) and (b): a. Mean life of a pump b. Variance of the life of a pump c. Wh...

Q: The time between calls is exponentially distributed with a mean time between

The time between calls is exponentially distributed with a mean time between calls of 10 minutes. a. What is the probability that the time until the first call is less than five minutes? b. What is th...

Q: Suppose that f (x) = 0.5x − 1

Suppose that f (x) = 0.5x − 1 for 2 < x < 4. Determine the following: a. P(X < 2.5) b. P(X > 3) c. P(2.5 < X < 3.5) d. Determine the cumulative distribution function of therandom variable. e. Determ...

Q: Suppose that X has a lognormal distribution with parameters θ = 0

Suppose that X has a lognormal distribution with parameters θ = 0 and ω2 = 4. Determine the following: a. P(10 < X < 50) b. Value for x such that P(X < x) = 0.05 c. Mean and variance of X

Q: Suppose that X has a lognormal distribution and that the mean and

Suppose that X has a lognormal distribution and that the mean and variance of X are 50 and 4000, respectively. Determine the following: a. Parameters θ and ω2 of the lognormal distribution b. Probabil...

Q: Asbestos fibers in a dust sample are identified by an electron microscope

Asbestos fibers in a dust sample are identified by an electron microscope after sample preparation. Suppose that the number of fibers is a Poisson random variable and the mean number of fibers per squ...

Q: The waiting time for service at a hospital emergency department follows an

The waiting time for service at a hospital emergency department follows an exponential distribution with a mean of three hours. Determine the following: a. Waiting time is greater than four hours b. W...

Q: A random variable X has the gamma distribution / a

A random variable X has the gamma distribution a. Show that the moment-generating function for t b. Find the mean and variance of X.

Q: The diameter of the dot produced by a printer is normally distributed

The diameter of the dot produced by a printer is normally distributed with a mean diameter of 0.002 inch. a. Suppose that the specifications require the dot diameter to be between 0.0014 and 0.0026 in...

Q: A square inch of carpeting contains 50 carpet fibers. The probability

A square inch of carpeting contains 50 carpet fibers. The probability of a damaged fiber is 0.0001. Assume that the damaged fibers occur independently. a. Approximate the probability of one or more da...