A lot of 1000 screws contains 30 that are defective. Two are
selected at random, without replacement, from the lot. Let A and B
denote the events that the first and second screws are defective,
respectively.
(a) Prove whether or not A and B are independent events using
mathematical expressions of probability.
20 Items were randomly selected from a large inventory. If 10%
of the items in the inventory are made in Asia,
1. What is the probability that exactly 4 of the 20 items
selected are made in Asia? (2 Points)
2. What is the probability that at most 4 of the 20 items
selected are made in Asia? (2 Points)
n chips manufactured, two of which are defective. k chips
randomly selected from n for testing.
Q1. What is Pr(a defective chip is in k selected chips) ?
n persons at a party throw hats in a pile, select at random.
Q2. What is Pr(no one gets own hat) ?
Q3. Plot Pr (no one gets own hat) in the Y-axis and n=[1,1000]
in the X-axis (~pmf)
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?
In a lot of 100 microcircuits, 20 are defective. Four
microcircuits are chosen at random to be tested.
Let X denote the number of tested circuits that are
defective.
a. Identify the distribution of X , including any parameters,
and find P(X = 2). You do not need to provide a decimal answer.
b. If appropriate (check), estimate P(X = 2) using an
appropriate method.
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.
We randomly chose 20 words from a randomly selected page in the
text of interest and counted the number of letters in each word: 5,
5, 2, 11, 1, 5, 3, 8, 5, 4, 7, 2, 9, 4, 8, 10, 4, 5, 6, 6. Suppose
the editor was hoping that the book would have a mean length of 6.5
letters. Does this sample indicate that the authors failed to meet
this goal?
Conduct a hypothesis test showing all 4 elements...
It is known that 20% of products on a production line are
defective. a. Randomly pick 5 products. What is the probability
that exactly 2 are defective? b. Products are inspected until first
defective is encountered. Let X = number of inspections to obtain
first defective. What is the probability that X=5?
Among 2200 randomly selected adult male passengers 1884 wear
seat belts. Among 2280 randomly selected adult female passengers
1999 wear seat belts. Use a 0.05 significance level to test the
claim that the rate of male passengers who wear seat belts is lower
than the rate of female passengers who wear seat belts.
H0: p1____p2 For Q35 (circle one: equal to, less than, greater
than, not equal to)
H1: p1____ p2 For Q36 (circle one: equal to, less than, greater...
A poll is taken in which 265 out of 1000 randomly selected
voters indicated their preference for a certain candidate. Find a
90% confidence interval. Remember σpˆ = ?pˆ(1−pˆ)
(a)
[4 pts] Find Zα/2:
(b)
[4 pts] Find the confidence interval:
(c)
[4 pts] Find the margin of error:
(d)
[4 pts] Without doing any calculations, indicate whether the
margin of error is larger or smaller or the same for a 95%
confidence interval. Why you think so?