Statistics and Probability Answers

A traffic engineer records a sample of the types of vehicles that cross a bridge. she counts 112 passenger cars, 18 light trucks, and 20 heavy trucks. she wants to make a spinner to model the probability of each type of vehicle crossing the bridge. Determine the percent of each sector of the spinner to the nearest percent. To the nearest tenth of a percent, what is the probability that at a given moment, a light truck crosses the bridge followed by a heavy truck?

From the previous data it is known that the length of time between customer complaints against a particular product (in months) is a gamma distribution with a 2 and 4. Changes are made. to tighten quality control requirements. After this change, 20 months passed before the first complaint. Does the tightening of quality control appear to be effective?

It is believed that there is a relationship between ‘level of information’ and ‘readiness to take a vaccination jab’ among tertiary institution students. To test this relationship, a research team decides to conduct a study using a sample of tertiary students.

Level of information Readiness score

7 7

9 6

9 6

2 3

8 9

5 7

7 6

6 7

8 6

10 9

1. Use the data supplied in a table to manually calculate the correlation coefficient (r). Show all your calculations
2. What does the ‘correlation coefficient’ that you calculated tell you about the direction and strength (magnitude) of the relationship between information and readiness? 
3. Calculate and interpret the coefficient of determination for this relationship

What does the ‘correlation coefficient’ that you calculated tell you about the direction and strength (magnitude) of the relationship between information and readiness? 

The Research Methods and Statistic module is almost over. Assume that the total marks were at an average of μ= 18 per assessment, and that the distribution of total marks are normally distributed with σ= 10.

What is the proportion that a student would have a mark more than 24 mark if randomly selected?

The Research Methods and Statistic module is almost over. Assume that the total marks were at an average of μ= 18 per assessment, and that the distribution of total marks are normally distributed with σ= 10. What proportion of students would have marks between 10 and 24? 

A normal distribution has μ = 80 and σ = 10. What is the probability of randomly selecting 75 < X < 85

A normal distribution has μ = 80 and σ = 10. What is the probability of randomly selecting between the mean and a score of 50

A normal distribution has μ = 80 and σ = 10. What is the probability of randomly selecting between the mean and a score of 90

A normal distribution has μ = 80 and σ = 10. What is the probability of randomly selecting X < 85