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Please advise,

I have attached some questions to this message, if someone could help me out with the answers with would be perfect.

Thank you!

**1. **

True or False. *Justify for full credit. *

- (a)Â If A and B are any two events, then P(A AND B) â‰¤ P(A OR B).
- (b)Â If the variance of a data set is 0, then all the observations in this data set must be zero.
- (c)Â The volume of milk in a jug of milk is 128 oz. The value 128 is from a discrete data set.
- (d)Â When plotted on the same graph, a distribution with a mean of 60 and a standard deviation
- of 5 will look less spread out than a distribution with a mean of 40 and standard deviation
- of 8.
- (e)Â In a left-tailed test, the value of the test statistic is -2. The test statistic follows a
- distribution with the distribution curve shown below. If we know the shaded area is 0.97, then we do not have sufficient evidence to reject the null hypothesis at 0.05 level of significance.

Choose the best answer. *Justify for full credit. *

**2. **

(a)

(b)

(i) (ii) (iii)

(i) (ii) (iii)

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

statistic

parameter

cannot be determined

The hotel ratings are usually on a scale from 0 star to 5 stars. The level of this measurement is

interval nominal ordinal

STAT 200: Introduction to Statistics Final Examination, Spring 2017 OL4/US2 Page 3 of 8

(iv) ratio

(c) The quality control department of a semiconductor manufacturing company tests every 100th product from the assembly line. This type of sampling is called:

(i) (ii) (iii) (iv)

cluster convenience systematic stratified

**3. **The frequency distribution below shows the distribution for IQ scores for a random sample of 1000 adults. (*Show all work. Just the answer, without supporting work, will receive no credit.) *

IQ Scores

Frequency

Cumulative Relative Frequency

50 - 69

23

70 - 89

249

90 -109

0.743

110 - 129

130 - 149

25

Total

1000

- (a)Â Complete the frequency table with frequency and cumulative relative frequency. Express the cumulative relative frequency to three decimal places.
- (b)Â What percentage of the adults in this sample has an IQ score between 90 and 129, inclusive?
- (c)Â Which of the following IQ score groups does the median of this distribution belong to?
- 70 â€“ 89, 90 â€“ 109, or 110 â€“ 129? Why?

**4. **The five-number summary below shows the grade distribution of a STAT 200 quiz for a sample of 160 students.

STAT 200: Introduction to Statistics Final Examination, Spring 2017 OL4/US2 Page 4 of 8

Answer each question based on the given information, and *explain *your answer in *each *case.

- (a)Â What is the interquartile range in the grade distribution?
- (b)Â Which of the following score bands has the fewest students?
- (i) 30-50
- (ii) 50 - 70
- (iii) 70 - 90
- (Iv) Cannot be determined
- (c)Â How many students in the sample are in the score band between 50 and 70?

**5. **Consider selecting one card at a time from a 52-card deck. What is the probability that the first card is an ace and the second card is also an ace? (Note: There are 4 aces in a deck of cards) (*Show all work. Just the answer, without supporting work, will receive no credit.) *

- (a)Â Assuming the card selection is with replacement.
- (b)Â Assuming the card selection is without replacement.

**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 50 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. Just the answer, without supporting work, will receive no credit.) *

- (a)Â Provide a written description of the complement event of (S OR P).
- (b)Â 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 sum of the two rolls is at most 6, and B be the event that the first one is a multiple of 3.

- (a)Â What is the probability that the sum of the two rolls is at most 6 given that the first one is a multiple of 3?
*Show all work. Just the answer, without supporting work, will receive no credit.* - (b)Â Are event A and event B independent? Explain.

**8. **Answer the following two questions. (*Show all work. Just the answer, without supporting work, will receive no credit). *

- (a)Â Mimi has seven books from the Statistics is Fun series. She plans on bringing three of the seven books with her in a road trip. How many different ways can the three books be selected?
- (b)Â UMUC Stat Club must appoint a president, a vice president, and a treasurer. There are 8 qualified candidates. How many different ways can the officers be appointed?

STAT 200: Introduction to Statistics Final Examination, Spring 2017 OL4/US2 Page 5 of 8

**9**. Let random variable *x *represent the number of heads when a fair coin is tossed two times.

- (a)Â Construct a table describing the probability distribution.
- (b)Â Determine the mean and standard deviation of
*x*. (Round the answer to two decimal places)

**10. **Mimi plans on growing tomatoes in her garden. She has 20 cherry tomato seeds. Based on her experience, the probability of a seed turning into a seedling is 0.60.

- (a)Â Let X be the number of seedlings that Mimi gets. 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)Â Find the probability that she gets at least 15 cherry tomato seedlings. (round the answer to 3 decimal places)
*Show all work. Just the answer, without supporting work, will receive no credit.*

**11. **The heights of pecan trees are normally distributed with a mean of 10 feet and a standard deviation of 2 feet. *Show all work. Just the answer, without supporting work, will receive no credit. *

- (a)Â What is the probability that a randomly selected pecan tree is between 9 and 12 feet tall? (round the answer to 4 decimal places)
- (b)Â Find the 80th percentile of the pecan tree height distribution. (round the answer to 2 decimal places)

**12. **Based on the performance of all individuals who tested between July 1, 2012 and June 30, 2015, the GRE Quantitative Reasoning scores are normally distributed with a mean of 152.47 and a standard deviation of 8.93. (https://www.ets.org/s/gre/pdf/gre_guide_table1a.pdf). *Show all work. Just the answer, without supporting work, will receive no credit. *

- (a)Â Consider all random samples of 36 test scores. What is the standard deviation of the sample means? (Round your answer to three decimal places)
- (b)Â What is the probability that 36 randomly selected test scores will have a mean test score that is between 148 and 152?
**A survey showed that 1200 of the 1600 adult respondents believe in global warming. Construct a 95% confidence interval estimate of the proportion of adults believing in global warming.***Show all work. Just the answer, without supporting work, will receive no credit.***A city built a new parking garage in a business district. For a random sample of 100 days, daily fees collected averaged $2,000, with a standard deviation of $500. Construct a 90% confidence interval estimate of the mean daily income this parking garage generates.***Show all work. Just the answer, without supporting work, will receive no credit.*

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