Statistics and Probability Answers

You are tasked with investigating whether fake news media platform and personality are independent. Consider the table below to help you with your task.
Celebrity. C/ Politician .P/ Sport Star .SS/ Total
Social Media .SM/ 1800 700 515 3015
Traditional Media. TM/ 485 350 150 985
Total 2285 1050 775 4000

Consider the statements below. Assume the level of significance is 1%
A. We reject the null hypothesis
B. We do not reject the null hypothesis
C. Media platform and personality are independent

Which statements are correct?
1. Only A
2. Only B
3. Only C
4. A and C Only
5. B and C only

There are three stations A, B & C with three communication links as,

a) If I cannot communicate between A & C, what is the probability that link 1 is failed.
b) If link 1 fails, what is the probability that I cannot communicate.

A news organization surveyed 80 adults. Each said he or she gets news from only one source. Here is a summary of their sources of news.
Source of news Number of adults
Internet 21
Newspaper 23
Radio 13
Television 23
Three of the adults from the survey are selected at random, one at a time without replacement. What is the probability that none of the three adults get news from the newspaper?
Do not round your intermediate computations. Round your final answer to three decimal places.

Literacy rate is a reflection of the educational facilities and quality of education available in a country, and mass communication plays a large part in the educational process. In an effort to relate the literacy rate of a country to various mass communication outlets, a demographer has proposed to relate literacy rate to the following variables: number of daily newspaper copies (per 1000 population), number of radios (per 1000 population), and number of TV sets (per 1000 population )
Determine mutiple regression

Dr. Xyz conducted a research study on the attitude of the online buyers in a certain district. The population size is 8,674. Determine the sample sizes using different methods of determining sample size.

Among the 250 employees of the local office of an international insurance company, 182 are whites, 51 are blacks, and 17 are Orientals. If we use proportional allocation to select a stratified random grievance committee of 15 employees, how many employees must we take from each race?

Life insurance salesman meets his prospective customers separately. At each meeting, he makes the same effort to persuade the prospective client to be insured. The vendor's understanding after a long term in the insurance business is that the probability of persuading the customer to be insured (probability of success) is 0,1. What is the probability in 4 trials to insure one of them?

Use R for computations in the following questions

The time between calls to a plumbing supply business is exponentially distributed with a
mean time between calls of 15 minutes.
(a) What is the probability that there are no calls within a 30-minute interval?
(b) What is the probability that at least one call arrives within a 10-minute interval?
(c) What is the probability that the rst call arrives within 5 and 10 minutes after opening?
(d) Determine the length of an interval of time such that the probability of at least one
call in the interval is 0.90.

Sarah Miney invests $10,000 in a certain stock at the beginning of the year. By
examining past movements of this stock and consulting with her broker, Sarah
estimates that the annual return from this stock, X, is normally distributed with
mean 5% and standard deviation 14%. Here X (when expressed as a decimal)
is the prot Sarah receives per dollar invested. It means that on December 31,
her $10,000 will have grown to $10; 000(1+X) dollars. Because Sarah is in the
33% tax bracket, she will then have to pay the Internal Revenue Service 33%
of her prot, if she earns a prot. However, she doesn
t have to pay any tax
if she loses money. Calculate the probability that Sarah will have to pay the
IRS at least $400, and calculate the probability that she won't have to pay any
tax. Also, calculate the dollar amount such that Sarah's after-tax prot is 90%
certain to be less than this amount; that is, calculate the 90th percentile of his
after-tax profit.

A survey shows that after production 5% of a packet of chips are underweight. If a sample of 20 packets were selected randomly, find the probability that at most 2 packets are underweight.