Reference no: EM132463843
Question 1
The breaking strength X of a concrete slab has a density function f(x)= Ae(-x/100)dx for breaking strength values in the range, 120 ≤ x ≤ 150.
a) Calculate the value of the constant A.
b) Plot the distribution in Maple (must show your code and output).
c) What is the probability that the concrete slab has a breaking strength between 130 and 150?
d) Find the average breaking strength.
e) Find the 80th percentile breaking strength.
Question 2
A film-coating process produces films whose thicknesses are normally distributed with a mean of 110 microns and a standard deviation of 10 microns. For a certain application, the minimum acceptable thickness is 90 microns.
a) What proportion of films will be too thin?
b) To what value should the mean be set so that only 1% of the films will be too thin?
c) If the mean remains at 110, what must the standard deviation be so that only 1% of the films will be too thin?
Question 3
A distributor receives a large shipment of components. The distributor would like to accept the shipment if 10% or fewer of the components are defective and to return it if more than 10% of the components are defective. She decides to sample 10 components, and to return the shipment if more than 1 of the 10 is defective.
a) If the proportion of defectives in the batch is in fact 10%, what is the probability that she will return the shipment?
b) If the proportion of defectives in the batch is 20%, what is the probability that she will return the shipment?
c) If the proportion of defectives in the batch is 2%, what is the probability that she will return the shipment?
d) The distributor decides that she will accept the shipment only if none of the sampled items are defective. What is the minimum number of items she should sample if she wants to have a probability no greater than 0.01 of accepting the shipment if 20% of the components in the shipment are defective?
Question 4
The article "Stochastic Estimates of Exposure and Cancer Risk from Carbon Tetrachloride Released to the Air from the Rocky Flats Plant" (A. Rood, P. McGavran, et al., Risk Analysis, 2001:675-695) models the increase in the risk of cancer due to exposure to carbon tetrachloride as lognormal with and .
(a) Find the mean risk.
(b) Find the median risk.
(c) Find the standard deviation of the risk.
(d) Find the 75th percentile.
Question 5
Suppose that under severe operating conditions the lifetime, in months, of a transistor is exponentially distributed with parameter
(a) Find the probability that such a transistor is between 4 and 10 months.
(b) Find the mean lifetime.
(c) Find the median lifetime.
(d) Find the standard deviation of the lifetimes.
(e) Find the 25th percentile of the lifetimes.
Question 6
Suppose that the random variable X has a Weibull distribution with parameters and Find:
a) The median of the distribution.
b) The lower quartile of the distribution.
c) P(0.5 ≤ x ≤ 1.5)