Statistics and Probability Answers

In a large population 63% of the people have been vaccinated if 5 people are randomly selected what is the probability that at least one of them has been vaccinated

Let X be a binomial(5, 0.2) random variable. Let Y be a discrete random variable that is independent of X, such that Y = 1 with probability 0.2 and Y = 0 with probability 0.8. What is the probability that the sum of X and Y is less than or equal to 3?

In a study of life expectancy of 400 people in a certain geographic region, the mean age death was 70 years, and the standard deviation was 5.1 years. If a sample of 50 people from this region is selected, what is the probability that he mean life expectancy will be less than 68 years?

A firm uses three local hotels to provide accommodations for its clients. From past experience, it is known that 20% of its client are assigned rooms at Hotel A, 45% at Hotel B and 35% at Hotel C. It is also known that the probabilities of Hotel A, Hotel B and Hotel C facing water problems are 0.02, 0.01 and 0.03 respectively.

(a)Draw a tree diagram for the above data

(b)What is the probability that a client will be assigned a room without water problem?

A university has analyzed the results of 1,000 students after the first year examinations. The result of the analysis is summarized below

Types of sponsorship

Examination results

Government

Private

Church

Students who were to be discontinued

155

150

105

Students who passed the examination

180

195

170

Students who were to sit for a supplementary paper

20

5

20

Required

The probability that a student was discontinued or was required to sit for a supplementary paper                                                                                                           

The probability that a student was a government sponsored           

The probability that a privately sponsored student passed the examination     

The probability that a student was church sponsored and was required to sit for a supplementary paper                                              

Percentile of 1.44 and - 1.34

Heights of the students in a class are given in the distribution below:

5' - 5'2"      10

5'2" - 5'4" 40

5'4" - 5'6"   25 .

Find:

1. Skewness and Kurtosis

X=28 ; n=100

A fast-food chain decided to carry out an experiment to assess the influence of advertising expenditure on sales. Different relative changes in advertising expenditure, compared to the previous year, were made in eight regions of the country, and resulting changes in sales levels were observed. The accompanying table shows the results

Increase in advertising expenditure (%) 0 4 14 10 9 8 6 1

Increase in sales (%) 2.4 7.2 10.3 9.1 10.2 4.1 7.6 3.5 

a. Estimate the least-squares the linear regression of the increase in sales on increase in advertising expenditure

b. Find a 90% confidence interval for the slope of the population regression line

Is the average amount spent on textbooks per semester by accounting majors significantly different from the average amount spent on text books per semester by management majors? Answer this question with a 90% confidence interval using the following data from random samples of students majoring in accounting or management. Discuss the assumptions

Accounting majors Management major

Mean $340 $285

Standard deviation 20 30

Sample size 40 50