Statistics and Probability Answers

In a certain manufacturing process, 10% of the articles manufactured are defective. Let  be the number of defective articles. If four articles are selected at random, what is the expected value of

Dr. Owino needs two students to help him with a science demonstration for his class of 18 girls and 12 boys. He randomly chooses one student who comes in front of classroom. He then chooses a second student from those still seated. What is the probability that both students chosen are girls? 

A gaussian random variable X has 𝜇𝑥 = 2, and 𝜎𝑥 = 2 . (a) Find P(X > 1.0). (b) Find P(X < −1.0).

Suppose a survey by the Department of Roads in 2019 revealed that 60% of the vehicles travelling on E to F Highway, where speed limits are posted at 80 kilometres per hour are found to be exceeding the limit. Suppose you randomly record the speed of 10 vehicles travelling on the highway as part of your internship. The sample size of the entire survey is not disclosed to you.

Compute the following probabilities. Showing all working.

a) P (X = 2).

b) P (X = 5).

c) P (X = 10).

A random sample of high school students are asked the number of hours they spent on social media. The hours are reported below: 3 5 6 7 8 10 12 13 14 15 You can assume the times are normally distributed with a standard deviation of 8.5.

a) Estimate with 90 percent confidence the mean number of hours spent on social media by all high school students. Show all working as part of your answer and interpret your answer.

Hypothesis test on population mean; 𝛼 = 0.01; two-tailed test; 𝑛 = 15; 𝜎 = 5 .

𝛼 = 0.01; two-tailed test; 𝑛 = 15; 𝜎 = 5 .

Consider a political discussion group consists of five democrats and six republicans. Four people are selected (at random) to attend a conference. In how many ways can four republicans be selected from the group?

Supposed the probability that a student will pass an Economics exam is 12, the probability that he will pass an Economics and Management exam is 35, and the probability that he will pass an Economics or a Management exam is 45. Find the probability that the student will pass a management exam.

Assume you found from the Annual Reports of the Local Police Station found that in a sample of 500 female reports on domestic violence over the 30-day period, 350 were not referred by the Women Crisis Centre. a) Based on the information provided, estimate 95 percent confidence interval for all the females who have been suggested to complain at the Local Police Station by the Crisis Centre. b) Interpret your findings.

Clients visiting a Chartered Accountant’s Firm on busy business day had to wait exactly 15 minutes less than an hour with a standard deviation of 10 minutes before they are able to see the Accountant. a) Compute the 90 percent confidence interval estimate for the average waiting time for all the clients visiting the office. Assume sample size is 36. b) Interpret your findings