Statistics and Probability Answers

Samples of 4 cards are drawn from a population of 6 cards numbered 1-6.

Construct a sampling distribution of the sample means and answer the following questions

1. How many sample of size 4 can be drawn from the population?

2.What are the possible means?

3.What is the probability of getting 4 as a mean?

4.What is the probability of getting 3.5 as a mean?

A group of students got the following scores in a test 6,9,12,15, and 21. Consider samples of size 3 that can be drawn from this population.

A. List all the possible samples and the corresponding mea.

B. Construct the sampling distribution of the sample means

A population consists of the five numbers 2,5,6, 8,and 11. Consider samples of size 2 that can be drawn from the population.

A. List the possible samples and the corresponding mean.

Consider a population consisting of 2, 4, 6, 8 and 10. Suppose samples of size 3 are drawn from this population.

a. Describe the sampling distribution of the sample means

b. What are the mean and variance of the sampling distribution of the sample means?

c. Construct a histogram for the sampling distribution.

A random sample of ten measurements were obtained from a normally distributed population with mean u=6.5. The sample values are X-4.2 and s 2.

a. Test the null hypothesis that the mean of the population against the alternative hypothesis, μ = 6.5. Use a = 0.05.

b. Test the null hypothesis that the mean of the population against the alternative hypothesis, u 6.5. Use a = 0.05

An insurance company found that 45% of all insurance policies are terminated before their maturity date. Assume that 10 polices are randomly selected from the company’s policy database. Assume a Binomial experiment.

Required:

a) What is the probability that eight policies are terminated before maturity?

b) What is the probability that at least eight policies are terminated before maturity?

c) What is the probability that at most eight policies are not terminated before maturity?

IQ tests are measured on a scale which is 𝑁(100,225). A woman wants to form an

“Computer Society” which only admits people with the top 1% of IQ scores. What would

she have to set as the cut-off point in the test to allow this to happen?

A bearing is selected a random and measured. The radius of ball bearings

produced by a particular process follow a normal distribution with y =

0.255 and g=0.001 inches. What is the probability that the radius is at

most 0.2545 in?

A scientist inoculates several mice, one at a time, with a disease germ until he finds 3 mice that have attacked by the disease. If the probability of getting attack of the disease is 1/5, what is the probability that 10 mice are required

A courier service company has found that their delivery time of parcels to clients is approximately normally distributed with a mean delivery time of 30 minutes and a variance of 25 minutes (squared).

Required:

a) What is the probability that a randomly selected parcel will take longer than 33 minutes to deliver?

b) What is the probability that a randomly selected parcel will take less than 26 minutes to deliver?

c) What is the minimum delivery time (minutes) for the 2.5% of parcels with the longest time to

deliver?

d) What is the maximum delivery time (minutes) for the 10% of the parcels with the shortest time to deliver?