8 sets of twins are entered in a competition. If 8
individuals are chosen at random, what is the probability none of
the chosen individuals are siblings?
An urn has 8 red and 12 blue balls. Suppose that balls are
chosen at random and removed from the
urn, with the process stopping when all the red balls have been
removed. Let X be the number of balls
that have been removed when the process stops.
a. Find P(X = 14)
b. Find the probability that a specifed blue ball remains in the
urn.
c. Find E[X]
Only 4% of items produced by a machine are defective. A random
sample of 200 items is selected and checked for defects.
a. Refer to Exhibit 7-1. What is the expected value for ?
b. What is the probability that the sample proportion will be
within +/-0.03 of
the population proportion
c.What is the probability that the sample proportion will be
between 0.04 and
0.07?
A machine in a factory has an error rate of 10 parts
per 100. The machine normally runs 24 hours a day and produces 30
parts per hour. Yesterday the machine was shut down for 4
A box contains 12 items, 4 of which are defective. An item is chosen at random and not replaced. This is continued until all four defec- tive items have been selected. The total number of items selected is recorded.
From a lot containing 25 items, 5 of which are defective, 4 are
chosen at random. Let X be the number of defective items found.
Obtain the probability distribution of X if (a) the items are
chosen with replacement, (b) the items are chosen without
replacement.
A production lot of 80 units has 8 defective items. We draw a random sample of 10 units and we want to know:
a.- the probability that the sample contains less than 3 defective articles
b.- the probability that the sample contains at least 3 good articles
c.- the probability that the sample contains more than 6 good articles
A lot of 100 items contains 10% which are defective and 90%
nondefective. Two are chosen at random. Let A = {the first item non
defective}, B = {the second item non defective}. Find P(B) and show
P(B) = P(A). Why is this?
A manufacturing company has purchased a new machine for $400,000
with a lifetime of 10-years. The increased net income due to this
machine is $90,000. The company’s tax rate is 40% and after-tax
MARR is 12%. The company is planning to use the machine for 8 years
and then sell it for $30,000. Develop tables using a spreadsheet to
determine the after-tax cash flow for each year from 1 through 8.
Calculate the after-tax PW and ERR after 8 years...