Questions from Applied Statistics

Q: The time for an automated system in a warehouse to locate a

The time for an automated system in a warehouse to locate a part is normally distributed with a mean of 45 seconds and a standard deviation of 30 seconds. Suppose that independent requests are made fo...

Q: The weight of a small candy is normally distributed with a mean

The weight of a small candy is normally distributed with a mean of 0.1 ounce and a standard deviation of 0.01 ounce. Suppose that 16 candies are placed in a package and that the weights are independen...

Q: Suppose that X and Y have a bivariate normal distribution with σX

Suppose that X and Y have a bivariate normal distribution with σX = 4, σY = 1, μX = 2, μY = 4, and ρ = −0.2. Draw a rough contour plot of the joint probability density function.

Q: A mechanical assembly used in an automobile engine contains four major components

A mechanical assembly used in an automobile engine contains four major components. The weights of the components are independent and normally distributed with the following means and standard deviatio...

Q: The permeability of a membrane used as a moisture barrier in a

The permeability of a membrane used as a moisture barrier in a biological application depends on the thickness of two integrated layers. The layers are normally distributed with means of 0.5 and 1 mil...

Q: Amarketing company performed a risk analysis for a manufacturer of synthetic fibers

Amarketing company performed a risk analysis for a manufacturer of synthetic fibers and concluded that new competitors present no risk 13% of the time (due mostly to the diversity of fibers manufactur...

Q: The continuous uniform random variable X has density function /

The continuous uniform random variable X has density function a. Show that the moment-generating function is b. Use MX(t) to find the mean and variance of X.

Q: Suppose X has a lognormal distribution with parameters θ and ω.

Suppose X has a lognormal distribution with parameters θ and ω. Determine the probability density function and the parameters values for Y = Xγ for a constant γ > 0. What is the name of this distribut...

Q: The power in a DC circuit is P = I2/R

The power in a DC circuit is P = I2/R where I and R denote the current and resistance, respectively. Suppose that I is approximately normally distributed with mean of 200 mA and standard deviation 0.2...

Q: The intensity (mW/mm2) of a laser beam on

The intensity (mW/mm2) of a laser beam on a surface theoretically follows a bivariate normal distribution with maximum intensity at the center, equal variance σ in the x and y directions, and zero cov...