Statistics and Probability Answers

In each of 4 races, the Democrats have a 60% chance of winning. Assuming that the races are independent of each other., what is the probability that:

Suppose we have a group of 50 TV’s and decide to sample 15. What is the probability that the 15 selected contain the best 5 TV’s? 

Maximum breadth of samples of male Egyptian skulls from 4000 B.C. and 150 A.D.

(based on data from Ancient Races of the Thebaid by Thomson and Randall-Maciver):

           4000 B.C. :     131 119 138 125 129 126 131 132 126 128 128 131 

           150 A.D. :       136 130 126 126 139 141 137 138 133 131 134 129 

Changes in head sizes over time suggest interbreeding with people from other regions.  Find the sample standard deviation and use a 90% confidence interval to determine whether the head sizes appear to have changed from 4000 B.C. to 150 A.D. Explain your result. 

A discrete random variable 𝑌 has a cumulative probability distribution as the table shown below.

𝑌 =𝑦 0 1 2 3

𝑃(𝑌 ≤ 𝑦) 5𝑘 10𝑘 11𝑘 12𝑘

(a) Determine the value of 𝑘.

(b) Calculate the expected value of 𝑌.

(c) Calculate the variance and standard deviation of 𝑌.

Polokwane Butchery supplies Vienna sausages in the entire of KZN province. An Inspector from

the CCSA has been skeptical of the mass of the Vienna sausage packs after receiving numerous

complaints. He wantsto investigate the marked massshown on Vienna sausages. A pilotstudy showed

a mean of 11.8kg per pack and a variance of 0.49kg. How many packs should the Inspector sample in

order to be 99% confident that the sample mean will differ by at most 0.2kg?

Assume that when adults with smartphones are randomly​ selected, 41​% use them in meetings or classes. If 3 adult smartphone users are randomly​ selected, find the probability that fewer than 3 of them use their smartphones in meetings or classes.

 The U.S. Department of Transportation reported that during November, 83.4% of Southwest Airlines’ flights, 75.1% of US Airways’ flights, and 70.1% of JetBlue’s flights arrived on time (USA Today, January 4, 2007). Assume that this on-time performance is applicable for flights arriving at concourse A of the Rochester International Airport, and that 40% of the arrivals at concourse A are Southwest Airlines flights, 35% are US Airways flights, and 25% are JetBlue flights.

a. Develop a joint probability table with three rows (airlines) and two columns (on-time arrivals vs. late arrivals).

b. An announcement has just been made that Flight 1424 will be arriving at gate 20 in concourse A. What is the most likely airline for this arrival?

c. What is the probability that Flight 1424 will arrive on time?

d. Suppose that an announcement is made saying that Flight 1424 will be arriving late. What is the most likely airline for this arrival? What is the least likely airline?

A local pharmaceutical company believes it has a 40% chance of being successful on bidding a contract with the Department of Health that yields a profit of 3,000,000 php. Assuming that it costs 500,000 php in consultancy fees to prepare the bid. What is the expected gain or loss for the company if it decides to bid on the contract?

Use the traditional method in testing the hypothesis in the problems below. In each problem, state the following:

a. State the hypotheses and identify the clam.

b. Find the critical value(s)

c. Find the test value

d. Make the decision

e. Summarize the result

First graders in the state of Virginia get an average score of 20 on a reading test (higher score reflect higher levels of performance). A teacher is using a new method to teach reading. She predicts that by the end of the first grade, students getting her new method will have significantly higher scores on reading than those in the population. The mean of the 25 students in her class is 23.2 and the standard deviation of the students in the class is 4.7. Do the data provide support for the teacher’s prediction?