Search & Filtering
According to Nielsen Media Research, approximately 67% of all U.S. households with television have cable TV. Seventy-four percent of all U.S. households with television have two or more TV sets. Suppose 55% of all U.S. households with television have cable TV and two or more TV sets. A U.S. household with television is randomly selected.
a. What is the probability that the household has cable TV or two or more TV sets?
b. What is the probability that the household has cable TV or two or more TV sets but not both?
c. What is the probability that the household has neither cable TV nor two or more TV sets?
d. Why does the special law of addition not apply to this problem?
A small company has 20 employees. Six of these employees will be selected randomly to be interviewed as part of an employee satisfaction program. How many different groups of six can be selected?
A company places a seven-digit serial number on each part that is made. Each digit of the serial number can be any number from 0 through 9.Digits can be repeated in the serial number. How many different serial numbers are possible?
A bin contains six parts. Two of the parts are defective and four are acceptable. If three of the six parts are selected from the bin, how large is the sample space? Which counting rule did you use, and why? For this sample space, what is the probability that exactly one of the three sampled parts is defective?
A supplier shipped a lot of six parts to a company. The lot contained three defective parts. Suppose the customer decided to randomly select two parts and test them for defects. How large a sample space is the customer potentially working with? List the sample space. Using the sample space list, determine the probability that the customer will select a sample with exactly one defect.
Consider all possible samples of size 4 (𝑛=4) taken with replacement from a population consisting of
the values 1, 3, and 5.
I. Compute the following:
1. Population Mean (μ)
2. Population Variance (𝜎²)
3. Population Standard Deviation (σ)
4. Mean of Sample Mean (μx̅)
5. Variance of Sample Mean (σ²x̅)
6. Standard Deviation of Sample Mean (σx̅)
One bag contains 6 red, 2 blue, and 3 yellow balls. A second bag contains 2 red, 4 blue, and 5 yellow balls. A third bag contains 3 red, 7 blue, and 1 yellow ball. One bag is selected at random. If 1 ball is drawn from the selected bag, what is the probability that the ball drawn is yellow?
A basket of fruits contains 8 apples and 10 oranges. Half of the apples and half of the oranges are rotten. If one fruit is chosen, what is the probability that a rotten apple or an orange is chosen?
One bag contains 6 red, 2 blue, and 3 yellow balls. A second bag contains 2 red, 4 blue, and 5 yellow balls. A third bag contains 3 red, 7 blue, and 1 yellow ball. One bag is selected at random. If 1 ball is drawn from the selected bag, what is the probability that the ball drawn is yellow?
Let X be a binomial variate with n=100, p=0.1. Find the approximate value of
P(10 ≤X≤ 12) using:
(i) normal distribution
(ii)poisson distribution
[You may like to use the following values.
P(Z ≤ 0.67)=0.7486, P(Z ≤ 0.33)=0.6293, P(Z ≤0)=0.5]
