INSTRUCTIONS: Attempt ALL questions

There are 30 students in a class. Among them, 8 students are learning both Audit and Tax. A total of 18 students are learning Audit. If every student is learning at least one language, how many students are learning Tax in total?

Among a group of students, 50 played cricket, 50 played hockey and 40 played volley ball. 15 played both cricket and hockey, 20 played both hockey and volley ball, 15 played cricket and volley ball and 10 played all three. If every student played at least one game, find the number of students and how many played only cricket, only hockey and only volley ball?

QUESTION THREE

Measures of dispersion are often used in finance as a proxy for risk. Explain.

1. A study was conducted to determine whether there were significant difference between medical students admitted through special programs (such as affirmative action) and medical students admitted through the regular admissions criteria. It was found that the graduation rate was 94% for the medical students admitted through special programs (based on data from the Journal of the American Medical Association).

(a) If 10 of the students from the special programs are randomly selected, find the probability that at least 9 of them graduated.

(b) Would it be unusual to randomly select 10 students from the special programs and get at most 7 of them graduated? Why or why not?

(c) Find the mean, variance and standard deviation.

(d) Is it unusual to have only 6 medical students from the special program graduated?

Three experiments investigating the relation between need for cognitive closure and persuasion were performed. Part of the study involved administering a "need for closure scale" to a group of students enrolled in an introductory psychology course. The "need for closure scale" has scores ranging from 101 to 201. For the 74 students in the highest quartile of the distribution, the mean score was x = 177.30. Assume a population standard deviation of σ = 7.61. These students were all classified as high on their need for closure. Assume that the 74 students represent a random sample of all students who are classified as high on their need for closure. Find a 95% confidence interval for the population mean score μ on the "need for closure scale" for all students with a high need for closure. (Round your answers to two decimal places.)

In 1995, the Educational Testing Service in Princeton, New Jersey (which administers SAT exam) re-centered the scores so that the overall mean would be approximately 1,000 in the combined math and verbal scores for a “large standardized group”. In 1996, approximately 1.1 million college-bound high school students took the exam and registered a mean score of 1,013, with a standard deviation of 222. About 40 percent of these students’ scores were between 900 and 1,100.
a) Based on this estimate, what is the probability that of 10 randomly selected students, less than four will be between 900 and 1,100?
b) What is the probability that more than four students will be in this range? What is the probability that exactly four students will be in this range?
c) What is the probability that between three and five students will range between 900 and 1,100?

A student researcher compares the heights of American students and non-American students from the student body of a certain college in order to estimate the difference in their mean heights. A random sample of 17 American students had a mean height of 70.8 inches with a standard deviation of 1.99 inches. A random sample of 12 non-American students had a mean height of 63.3 inches with a standard deviation of 2.63 inches. Determine the 90% confidence interval for the true mean difference between the mean height of the American students and the mean height of the non-American students. Assume that the population variances are equal and that the two populations are normally distributed. Step 2 of 3 : Find the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.

Three experiments investigating the relation between need for cognitive closure and persuasion were performed. Part of the study involved administering a "need for closure scale" to a group of students enrolled in an introductory psychology course. The "need for closure scale" has scores ranging from 101 to 201. For the 83 students in the highest quartile of the distribution, the mean score was x = 177.30. Assume a population standard deviation of σ = 7.69. These students were all classified as high on their need for closure. Assume that the 83 students represent a random sample of all students who are classified as high on their need for closure.

Find a 95% confidence interval for the population mean score μ on the "need for closure scale" for all students with a high need for closure. (Round your answers to two decimal places.)

lower limit'

upper limit

Three experiments investigating the relation between need for cognitive closure and persuasion were performed. Part of the study involved administering a "need for closure scale" to a group of students enrolled in an introductory psychology course. The "need for closure scale" has scores ranging from 101 to 201. For the 79 students in the highest quartile of the distribution, the mean score was x = 176.50. Assume a population standard deviation of σ = 7.47. These students were all classified as high on their need for closure. Assume that the 79 students represent a random sample of all students who are classified as high on their need for closure. Find a 95% confidence interval for the population mean score μ on the "need for closure scale" for all students with a high need for closure. (Round your answers to two decimal places.)

lower limit

upper limit

Three experiments investigating the relation between need for cognitive closure and persuasion were performed. Part of the study involved administering a "need for closure scale" to a group of students enrolled in an introductory psychology course. The "need for closure scale" has scores ranging from 101 to 201. For the 84 students in the highest quartile of the distribution, the mean score was x = 178.30. Assume a population standard deviation of σ = 7.47. These students were all classified as high on their need for closure. Assume that the 84 students represent a random sample of all students who are classified as high on their need for closure. Find a 95% confidence interval for the population mean score μ on the "need for closure scale" for all students with a high need for closure. (Round your answers to two decimal places.)

A study was conducted to determine whether there were significant differences between medical students admitted through special programs (such as retention incentive and guaranteed placement programs) and medical students admitted through the regular admissions criteria. It was found that the graduation rate was 91.5% for the medical students admitted through special programs.

If 10 of the students from the special programs are randomly selected, find the probability that at least 9 of them graduated.
round your answer to 4 decimal places
prob =

If 10 of the students from the special programs are randomly selected, find the probability that eactly 7 of them graduated.
round your answer to 4 decimal places
prob =

Would it be unusual to randomly select 10 students from the special programs and get exactly 7 that graduate?

• yes, it is unusual
• no, it is not unusual

If 10 of the students from the special programs are randomly selected, find the probability that at most 7 of them graduated.
round your answer to 4 decimal places
prob =

Would it be unusual to randomly select 10 students from the special programs and get at most 7 that graduate?

• yes, it is unusual
• no, it is not unusual