Statistics and Probability Answers

From year to year, It has been observed that there is a greater number of women who are graduating from college, RAPA university noted that in 2015, 40% of their college graduates were women. Supposed a random sample of 120 graduating college students this year were selected. Of this number 57 were women. That this indicate that the proportion of college graduates that are women this year is significantly higher than the proportion in 2015? Use the rejection region approach using 0.10 level of significance

1)     It has been determined that 4% of drivers checked at a road stop show traces of alcohol and 11% of drivers checked do not wear seat belts. In addition, it has been observed that the two infractions are independent of one another. 

A)  Calculate the probability that none of the drivers show traces of alcohol.

Suppose that when a new machine is functioning well, 92% of the items produced are nondefective. Assume that a random sample of five parts produced on the machine is selected and we are interested in the number of defective parts found.

Required:

a) What are the conditions for this experiment to be considered a binomial experiment? Motivate. (8)

Page 13 of 14 b) What is the probability that all parts selected will be defective?

(3)

c) What is the probability that none of the parts selected will be defective?

d) What is the probability that more than five parts will be defective?

e) What is the probability that at least three parts will be non-defective?

In a lottery, players must match five numbers plus a bonus number. Five white balls are chosen from 59 white balls numbered from 1 to 59, and one red ball (the bonus number) is chosen from 35 red balls numbered 1 to 35,how many different results are possible?

A pollster wishes to estimate the true proportion of U.S. voters who oppose capital punishment. How many voters should be surveyed in order to be 95% confident that the true proportion is estimated to be within 5%?

 A new gas-electric hybrid car has recently hit the market. The distance traveled on 1 gallon of fuel is normally distributed with a mean of 65 miles and a standard deviation of 4 miles. Find the probability of the following events. (show the concerned region by z curve) 1. The car travels more than 70 miles per gallon. 2. The car travels less than 60 miles per gallon. 3. The car travels between 55 and 70 miles per gallon.

The time it takes a randomly selected employee to perform a task is normally distributed with a mean value of 120 seconds and a standard deviation of 20 seconds.

Calculate the probability that a randomly selected employee will complete:

1. The task within 100 to 130 seconds

2. In more than 75 seconds

Question 2

The table below shows whether students are left handed or right handed by sex. The total number of students who were interviewed was 100. The responses was as follows;

Male Female Total

Righ habded 38 42 80

Left handed 12 8 20

Total 50 50 100

1. What is the probability of selecting a left-handed male?

2. What is the probability of selecting a right-handed female?

find the standard probabilities of:

1) 2.5P20

2) 2.5q20

3) 2.5/q20

Given that the force of mortality for a survival model is given by the formula:

u(x) = 0.9/90-x

find the standard probabilities of:

1) 2.5P20

2) 2.5q20

3) 2.5/q20

Given that the force of mortality for a survival model is given by the formula:

u(x) = 0.9/90-x

Based on the research conducted by the DOH, “63 % of those found to have diabetes were not aware that they have such disease”. The statement above is an example of _____________.