STAT 200 Complete Solution

Answer all 10 questions. Make sure your answers are complete. Show all of your work and supporting reasoning for your answers. All answers must be manual calculations. No separate Excel sheets or calculator print outs. 

1. True or False. Justify fully

(a) If all the observations in a data set are identical, then the variance for this data set is zero. 

(b) If A and B are disjoint, P(A) = 0.4 and P(B) = 0.5, then P(A AND B) = 0.2. 

(c) The mean is always equal to the median for a normal distribution. 

(d) A 95% confidence interval is wider than a 98% confidence interval of the same parameter.

 (e) It’s easier to reject the null hypothesis in a hypothesis test at 0.05 significance level than at 0.01 significance level. 

2. For each section choose the best answer. Justify fully
(a) A study was conducted at a local college to analyze the average GPA of students graduated from UMUC in 2016. 100 students graduated from UMUC in 2016 were randomly selected, and the average GPA for the group is 3.5. The value 3.5 is a
(i)    statistic 
(ii)    parameter 
(iii)    cannot be determined 

(b) The hotel ratings are usually on a scale from 0 star to 5 stars. The level of this measurement is 
(i) interval 
(ii) nominal 
(iii) ordinal 
(iv) ratio 
(c) On the day of the Virginia Primary Election, UMUC News Club organized an exit poll at three polling stations were randomly selected and all voters were surveyed as they left those polling stations. This type of sampling is called: 
(i) cluster 
(ii) convenience 
(iii) systematic 
(iv) stratified

3. A random sample of 100 students was chosen from UMUC STAT 200 classes. The frequency distribution below shows the distribution for study time each week (in hours). (Show all work). 

 
(a) Complete the frequency table with frequency and relative frequency. Express the relative frequency to two decimal places. 

(b) What percentage of the study times was at least 15 hours? 

(c) In what class interval must the median lie? 5.0 – 9.9, 10.0 -14.9, 15.0 – 19.9, or 20.0 – 24.9? Why?

4. The five-number summary below shows the grade distribution of a STAT 200 quiz for a sample of 60 students.

See Next page

Answer each question based on the given information, and explain your answer in each case. (Show all work fully)

(a) What is the range in the grade distribution? 

(b) Which of the following score bands has the most students? 
(i) 30 – 50
(ii) 50 – 70
(iii) 85 - 100 
(Iv) Cannot be determined 

(c) How many students in the sample are in the score band between 65 and 100?

5. A basket contains 3 white balls, 2 yellow balls, and 5 red balls. Consider selecting one ball at a time from the basket. (Show all work). 

(a) Assuming the ball selection is with replacement. What is the probability that the first ball is white and the second ball is also white? 

(b) Assuming the ball selection is without replacement. What is the probability that the first ball is yellow and the second ball is red?
6. There are 1000 juniors in a college. Among the 1000 juniors, 300 students are taking STAT200, and 150 students are taking PSYC300. There are 100 students taking both courses. Let S be the event that a randomly selected student takes STAT200, and P be the event that a randomly selected student takes PSYC300. (Show all work) 
(a) Provide a written description of the complement event of (S OR P). 

(b) What is the probability of complement event of (S OR P)?

7. Consider rolling a fair 6-faced die twice. Let A be the event that the product of the two rolls is at most 5, and B be the event that the first one is a multiple of 3. 

(a) What is the probability that the product of the two rolls is at most 5 given that the first one is a multiple of 3? Show all work.

(b) Are event A and event B independent? Fully Explain.

8. Answer the following two questions. (Show all work fully). 

(a) A bike courier needs to make deliveries at 6 different locations. How many different routes can he take?
(b) Mimi has eight books from the Statistics is Fun series. She plans on bringing three of the eight books with her in a road trip. How many ways can the three books be selected? (Show all work and explain)

9. Let random variable x represent the number of heads when a fair coin is tossed three times. (Show all work)
(a) Construct a table describing the probability distribution.

(b) Determine the mean and standard deviation of x. (Round the answer to two decimal places)

10. Mimi just started her tennis class three weeks ago. On average, she is able to return 20% of her opponent’s serves. Assume her opponent serves 8 times. 
(a) Let X be the number of the serves that Mimi returns. As we know, the distribution of X is a binomial probability distribution. What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively? 
(b) Find the probability that that she returns at least 1 of the 8 serves from her opponent. (round the answer to 3 decimal places) Show all work.