An engineering school reports that 55% of its students are male (M), 37% of its students are between the ages of 18 and 20 (A), and that 30% are both male and between the ages of 18 and 20. What is the probability of a random student being chosen who is a female and is not between the ages of 18 and 20? Your answer should be to two decimal places.

An engineering school reports that 50% of its students were male (M), 39% of its students were between the ages of 18 and 20 (A), and that 34% were both male and between the ages of 18 and 20. What is the probability of choosing a random student who is a female or between the ages of 18 and 20? Assume P(F) = P(not M). Your answer should be given to two decimal places.

Imagine that you are taking a very difficult test (in a statistics class of course), historically the mean grade is 43.5 out of 100 with a standard deviation of 15.2. Treating the historical average and standard deviation as parameters of a normal curve:

A.) What is the probability of passing with a score of 60 or higher.

B.) What is the probability of getting an A- (90 to 92.5)

C.) If a new class of 35 students takes the test, how many students in the new class would you expect to get a B (80 to 89) ?

D.) Given your results assume that we actually gave such a test to 10 sections (of ten students each) and discovered that the average number of students getting an A on the exam in each section was 7. Using your knowledge of probability what can you suggest about this situation ?

Many University campuses sell parking permits to their students allowing them to park on campus in designated areas. Although most students complain about the relatively high cost of these permits, what annoys many of these students even more is that after having paid for their permits, vacant parking spaces in the designated lots are very difficult to find during much of the day. Many end up having to park off campus anyway, where permits are not required. Assuming the University is unable to build new parking facilities on campus due to insufficient funds, what recommendation might you propose that would remedy the problem of students with permits being unable to find places to park on campus? (Hint: Think in terms of demand and supply analysis and how a market functions.)

Exercise 3

The data in the table represent the "Exam Scores" for two random samples of students. The first group of n1 = 6 students were under active-learning course, and the second group of n2 = 6 students were under traditional lecturing. Note that the standard deviations in the Active group is s1= 3.43 and in the Traditional group is s2 = 3.03.

Please answer the following questions underneath each question.

1. Which test is appropriate to compare the Exam-Scores in the two groups of students?

Answer:

2. Conduct the steps of this test

(please enumerate and write all the steps of your answer below)

Step 1:

3. State your conclusion in the context of this study

A student set out to see if female students spend more time studying than male students. He randomly surveyed 30 females and 30 males and asked them how much time they spend studying, on average, per day. The data is obtained is shown below.

H0: mean study time for females = mean study time for males

H1: mean study time for females > mean study time for males

1. Are there any assumptions that we must make about the two populations (female students / male students) before we proceed?

The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean μ=535.4 and standard deviation σ=28.

(a) What is the probability that a single student randomly chosen from all those taking the test scores 542 or higher?
ANSWER:

For parts (b) through (d), consider a simple random sample (SRS) of 25 students who took the test.

(b) What are the mean and standard deviation of the sample mean score x, of 25 students?
The mean of the sampling distribution for x is:
The standard deviation of the sampling distribution for x is:

(c) What z-score corresponds to the mean score x of 542?
ANSWER:

(d) What is the probability that the mean score x of these students is 542 or higher?
ANSWER:

According to a recent survey, women chat on their mobile phones more than do men. To determine if the same patterns also exist in colleges, Irina takes a random sample of 40 male students and 40 female students in her college. She finds that female students chatted for a sample average of 820 minutes per month, with a sample standard deviation of 160 minutes. Male students, on the other hand, chatted for a sample average of 760 minutes per month, with a sample standard deviation of 240 minutes. It is not reasonable to assume equal population variances. Do the same patterns appear to exist in college? Conduct an appropriate test to answer this question, using the .05 level of significance. Please complete all steps in the test process and please show all work.

Consider the variable x = time required for a college student to complete a standardized exam. Suppose that for the population of students at a particular university, the distribution of x is well approximated by a normal curve with mean 50 minutes and standard deviation 5 minutes. (Use a table or technology.)

(a)

If 55 minutes is allowed for the exam, what proportion of students at this university would be unable to finish in the allotted time? (Round your answer to four decimal places.)

(b)

How much time (in minutes) should be allowed for the exam if you wanted 90% of the students taking the test to be able to finish in the allotted time? (Round your answer to one decimal place.)

min

(c)

How much time (in minutes) is required for the fastest 25% of all students to complete the exam? (Round your answer to one decimal place.)

min

The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean μ=531.5μ=531.5 and standard deviation σ=29.6σ=29.6.

(a) What is the probability that a single student randomly chosen from all those taking the test scores 536 or higher?
ANSWER:  

For parts (b) through (d), consider a random sample of 25 students who took the test.

(b) What are the mean and standard deviation of the sample mean score x¯x¯, of 25 students?
The mean of the sampling distribution for x¯x¯ is:  
The standard deviation of the sampling distribution for x¯x¯ is:

(c) What z-score corresponds to the mean score x¯x¯ of 536?
ANSWER:

(d) What is the probability that the mean score x¯x¯ of these students is 536 or higher?
ANSWER:  

A student researcher compares the ages of cars owned by students and cars owned by faculty at a local state college. A sample of 233 cars owned by students had an average age of 6.62 years. A sample of 280 cars owned by faculty had an average age of 7.94 years. Assume that the population standard deviation for cars owned by students is 2.13 years, while the population standard deviation for cars owned by faculty is 3.14 years. Determine the 90% confidence interval for the difference between the true mean ages for cars owned by students and faculty.

Step 1 of 2:

Find the critical value that should be used in constructing the confidence interval.

Step 2 of 2:

Construct the 90% confidence interval. Round your answers to two decimal places