In October 2024
Search & Filtering
A population consists of the five numbers 2, 3, 6, 8, and 11.
Consider the samples of size 2 that can be drawn from this
population.
A. List all the possible samples and the corresponding mean.
B. Construct the sampling distribution of the sample mean.
Suppose that the racial/ethnic distribution in a large city is given by the table that follows.
Black Hispanic Other
20% 15% 65%
Suppose that a jury of twelve members is chosen from this city in such a way that each resident has an equal probability of being selected independently of every other resident.
Lets find probability that the jury contains:
a. three Black, two Hispanic, and seven other members.
b. four Black and eight other members.
c. at most one Black member.
Two chess players have the probability Player A would win is 0.40, Player B would win is 0.35, game would end in a draw is 0.25. If these two chess players played 12 games, what is the probability that Player A would win 7 games, Player B would win 2 games, the remaining 3 games would be drawn?
The probabilities of a machine manufacturing 0,1,2,3 and 5 defective parts in one day are 0.75,0.17,0.04,0.025,0.01 and 0.005 respectively.Find the mean of the probability distribution.
80% of all business startups in the IT industry report that they generate a profit in their first year. If a sample of 10 new IT business startups is selected, find the probability that exactly seven will generate a profit in their first year.
Two chess players have the probability Player A would win is 0.40, Player B would win is 0.35,
game would end in a draw is 0.25. If these two chess players played 12 games, what is the probability that Player A would win 7 games, Player B would win 2 games, the remaining 3 games would be drawn?
In a restaurant an average of two out of every five customers asks for water with their meal. A family
of ten members arrives in the restaurant. What is the probability that:
a. Exactly seven members ask for water?
b. Less than nine members ask for water?
Suppose a researcher goes to a small college of 200 faculty, 12 of which have blood type O-negative. She obtains a simple random sample of the faculty. Let the random variable X represent the number of faculty in the sample of size that have blood type O-negative.
a. What is the probability that 3 of the faculty have blood type O-negative?
b. What is the probability that at least one of the faculty has blood type O-negative?
Usman rolls two dice colored purple and yellow simultaneously. The random variables X and Y are
defined as follows:
X = The number showing on the purple die.
Y = The number of dice that show the number six.
For example, if the purple and yellow dice show the numbers 6 and 4, then X = 6 and Y = 1.
a. Write down a table showing the joint probability mass function for X and Y.
b. Find the marginal distribution for X and Y.
c. Compute E(X) and E(Y).
d. Find the covariance of X and Y.
e. Find the correlation coefficient of X and Y.
An auto battery company claims that their batteries’ mean
life is 50 months. In order to check this claim, a DTI
researcher took a random sample of 18 of these batteries
and found that the mean life is 48.8 months with a
standard deviation of 7 months. Assume that battery life
follows a normal distribution, test with 90% confidence
whether the companies’ claim is different from the true
#339914 on Dec 2023