A professor of a introductory statistics class has stated that, historically, the distribution of final exam grades in the course resemble a normal distribution with a mean final exam mark of 60% and a standard deviation of 9%.
(a) What is the probability that a randomly chosen final exam mark in this course will be at least 75%?
(b) In order to pass this course, a student must have a final exam mark of at least 50%. What proportion of students will not pass the statistics final exam?
(c) The top 2% of students writing the final exam will receive a letter grade of at least an A in the course. To four decimal places, find the minimum final exam mark needed on the statistics final to earn a letter grade of at least an A in the course.

Statistics))

1.The Round-trip-time between the college and home for a student is normally distributed with a mean of 47 min and a standard deviation of 4.6 min. To one-decimal place, what Round-trip-time would be considered the 70th percentile? Make sure to include units.

2.A recent study showed that the average amount of time spent doing part time job by students at a college is 29 hours per week with a standard deviation of 3.8 hours. If 64 students were selected at random, what is the probability that their average weekly working hours will be less than 20 hours?Round answer to two decimals, if necessary.Express answer in percent. Don't forget to put % sign with you answer.

COIN TOSSES In a large class of introductory Statistics students, the professor has each student toss a coin 16 times and calculate the proportion of his or her tosses that were heads. The students then report their results, and the professor plots a histogram of these several proportions.

1. What shape would you expect this histogram to be? Why?

2. Where do you expect the histogram to be centred?

3. How much variability would you expect among these proportions?

4. Explain why a Normal model should not be used here.

The answer is

1, symmetric

2, 0.5

3, 0.125

4. np=8<10

Please explain why the third question has answer 0.125. how did you get it?

Currently students have several popular fast food options (e.g. Chick fil A, Wendy’s, Papa Johns, Au Bon Pain), cafeterias (Muse, Dalton), and take out (Hisso Sushi, Pinkberry).  Currently Chartwell Food Services is the licensed operator for all food options on campus.  The company has developed a short 10-minute survey to complete in whatever manner would produce the best results.     Research questions involve the most preferred food vendors, most preferred food types, preferred locations, and price points.  Develop a sampling plan that would yield generalizable results regarding the lunch and dinner habits of Radford University students.  Explain your choices.

Word Problems with a Sample Data Set:

1. A sample of Full-time SUNY Poly students were asked how many credit hours they were taking this semester and the following information was obtained. Assume credit hours are approximately normally distributed.

16        18        12        17        20        18        15        14

*Round all final answers to 2 decimal places if necessary

1. Construct a 90% confidence interval for the population mean

2. Construct a 95% confidence interval for the population standard deviation

3. SUNY Poly claims that all their students average less than 18 credit hours per semester. Test SUNY’s claim at α = 0.05, what can you conclude about the claim?

The heights of female students at a university follows Normal distribution with a mean 66 inches and a standard deviation 3 inches. A researcher randomly selects 36 female students from the university, surveys their heights and calculates a sample mean.

Now suppose that the population standard deviation is unknown. Also, the researcher calculate the sample standard deviation to be 3 inches.

a) What is the probability that the sample mean height is between 65 inches and 67 inches?

b) Instead of 36, suppose the sample size is 64 only for this sub-question. Then what is the probability that the sample mean height is between 65 inches and 67 inches?

Please answer in excel format if possible! And show the function! Thank youuuu

Let the random variable X represent a student’s score on an IQ test. Suppose that student IQ scores are Normally distributed with a mean of 100 and a standard deviation of 15.

Part A.Any student who scores at least 130 on an IQ test would be considered gifted. If a student has scored 130 on an IQ test, what percentile does this score represent? Part B.In a class of 50 students, how many would you expect to score at least 115 on an IQ test?

Part C.Suppose that 10 students are randomly selected from a large school. What is the chance that at least 3 of them will have an IQ score greater than 125 (use binomial PMF)

A random sample of 28 statistics tutorials was selected from the past 5 years and the percentage of students absent from each one recorded. The results are given below. Assume the percentages of students' absences are approximately normally distributed. Use Excel to estimate the mean percentage of absences per tutorial over the past 5 years with 90% confidence. Round your answers to two decimal places and use increasing order.

Number of Absences

13.9

16.4

12.3

13.2

8.4

4.4

10.3

8.8

4.8

10.9

15.9

9.7

4.5

11.5

5.7

10.8

9.7

8.2

10.3

12.2

10.6

16.2

15.2

1.7

11.7

11.9

10.0

12.4

A researcher plans to do an experiment in the college setting concerning the effects of class size on attendance in a first year law course. He has four levels of size, namely, 15, 25, 40, and 60 students. Four colleges are involved in the study, each having eight first-year law classes, two of each class size. The researcher can assign students at random to a class within a college. All professors teach four classes; the dependent variable is grades measured after one semester. Discuss the problems of control in this situation. Consider possible uncontrolled variables and variables that are or might be controlled. Is there a possibility of confounding variables in this research situation? State one or more hypotheses for this experiment.