Statistics and Probability Answers

1.    Find 95% confidence limits for the mean of a normally distributed population from which the following samples was taken 15,17,10,18,16,9,7,11,13,14.

If the measure of systolic blood pressure is normally distributed with a mean of 120 and a standard deviation of 10, find the probability that a randomly selected person will have a systolic blood pressure below 130. Assume systolic blood pressure is normally distributed.

1. Of the students in the college, 60% of the students reside in the hostel and 40% of the students are day scholars. Previous year result reports that 30% of all students who stay in the hostel scored A Grade and 20% of day scholars scored A grade. At the end of the year, one student is chosen at random and found that he/she has an A grade. What is the probability that the student is a hostlier? 

2. Two players A and B are competing at a trivia quiz gameinvolving a series of questions. On any individual question, the probabilities that A and B give the correct answer areαandβrespectively, for all questions, with outcomes for different questions being independent. The game finishes when a player wins by answering a question correctly. Compute the probability that A wins if

a) A answers the first question, 

b) B answers the first question.

Based on a​ poll, 60​% of adults believe in reincarnation. Assume that 6 adults are randomly​ selected, and find the indicated probability. What is the probability that all the selected adults believe in reincarnation

Assume the machine shifts and is filling the vials with a mean amount of 9.96 milligrams and a standard deviation of 0.05 milligram. You select five vials and find the mean amount of compound added.

Allie, Barry, and Cassie—the three children in the Smith family—have dishwashing responsibilities. Every day, their mother randomly chooses a child to wash dishes after dinner.

Develop a model that their mother could use to choose which child will wash dishes after dinner. You may want to consider spinners, number cubes, or coins.

Explain why your model can be used to predict which child will wash dishes after dinner.

Allan wants to randomly choose a pair of pants and a shirt from his closet. The list below shows all possible combinations of pants and shirts, where the first color is for the pants and the second color is for the shirt.

(blue, black)

(blue, blue)

(blue, green)

(blue, green)

(black, black)

(black, blue)

(black, green)

(black, green)

If Allan randomly chooses a pair of pants and a shirt, what is the probability that Allan will choose a black pair of pants and a blue shirt?

Identify a pants-and-shirt combination that has a 1

4

14 probability of being randomly chosen.

Andre is waiting for the school bus. He knows that 2 out of 6 cars in his town are white. He wants to determine the probability that at least two white cars drive by in a row. He uses a number cube as a simulation. He lets the numbers 1 and 2 represent a white car and lets all other numbers represent a car that is not white. He rolls the number cube 6 times and records the outcomes in the table below.

1. A charity group raises funds by collecting waste paper. A skip-full will contain an 

amount, X, of other materials such as plastic bags and rubber bands. X may be regarded 

as a random variable with probability function

𝑓(𝑥) = {𝑘(𝑥 − 1)(4 − 𝑥) , 1 < 𝑥 < 4

0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

 (All numerical values in this question are in units of 100kg,)

i )Show that 𝑘 =1/2.

 ii)Find the mean and the standard deviation of X.

3. A research was conducted in 2017 at the Tema Port to find the ages of cars imported into 

the country. According to the research, 10% of the cars imported were less than one-year￾old. Assuming this result holds true for the current period for all cars imported into the 

country.

Find the probability that in a random sample of 5 cars at the Tema Port

(i) exactly 3 are less than one-year-old.

(iii) none is less than one-year-old 

(iv) Find the mean and standard deviation of the distribution if a random 

 Sample of 200 cars were selected

A researcher studying genetic influences on learning compares the maze performance of four genetically different strains of mice, using eight mice per strain. Performance for the four strains were as follows: