Statistics and Probability Answers

3. Consider a normal distribution with a mean of 500 and a standard deviation of 50.
a. Below what value can we expect to have the lowest 20%?
b. Between what values can we expect to find the middle 80%?

QUESTION B1

A study of corruption for a certain geographic region showed an average of 5 corruptions occur per 20,000 people. In a city of 80,000 people, find the probability that at least 3 corruptions occur.

QUESTION B2

(a) A random sample of 300 students from a geographic area indicated that 45 students attended private school. Estimate the true proportion of students attending private schools with 95% confidence.

(b) A survey of 25 individuals who passed the ACCA exam showed that average annual
salary is RM150,000 and standard deviation RM15,000.

(i) Find the degrees of freedom.

(ii) Construct 99% confidence interval for the true average salary.

If the standard deviation of a national accounting examination is 32, how large a sample is needed to estimate the true mean score within 5 points with 98% confidence?

QUESTION B1

A study of corruption for a certain geographic region showed an average of 5 corruptions occur per 20,000 people. In a city of 80,000 people, find the probability that at least 3 corruptions occur.

QUESTION B2

(a) A random sample of 300 students from a geographic area indicated that 45 students attended private school. Estimate the true proportion of students attending private schools with 95% confidence.

(b) A survey of 25 individuals who passed the ACCA exam showed that average annual
salary is RM150,000 and standard deviation RM15,000.

(i) Find the degrees of freedom.

(ii) Construct 99% confidence interval for the true average salary.

A study of 35 gamers showed that their average score on a particular game was 90 and
the population standard deviation is 5.
(i) Find the best point estimate of the population mean.

(ii) Find the 95% confidence interval of the mean score for all gamers.

(iii) Find the 95% confidence interval of the mean score if a sample of 70 gamers is
used instead of a sample of 35.

(iv) From your answer in part (ii) and (iii), which interval is smaller?

Ministry of Higher Education (MOHE) put a guideline that maximum of 30% students are allowed to be in campus to control the spread of Covid-19. In average, 13 students will come to Statistics class with standard deviation of 3 students. A sample of 20 students are chosen. Find probability that the average number of students come to Statistics class is less than 15?

(a) A random sample of 300 students from a geographic area indicated that 45 students attended private school. Estimate the true proportion of students attending private schools with 95% confidence.

(b) A survey of 25 individuals who passed the ACCA exam showed that average annual
salary is RM150,000 and standard deviation RM15,000.
(i) Find the degrees of freedom.
(ii) Construct 99% confidence interval for the true average salary.

A study of corruption for a certain geographic region showed an average of 5 corruptions occur per 20,000 people. In a city of 80,000 people, find the probability that at least 3 corruptions occur.

For a group of 100 men subjected to a stress situation, the mean number of heart beats per minute was 130, and the standard deviation was 5. Find the 90% confidence interval of the true mean.

a) A university wishes to estimate the average number of hours students spend doing homework per week. The variance obtained from previous study is 25 hours. How large a sample must be selected if they want to be 98% confident of finding the true mean given the error is within 1.5 hours?
(b) Find t value for a 95% confidence interval when the sample size is 8.