STAT200 2023 GE3

docx

School

University of Delaware *

*We aren’t endorsed by this school

Course

200

Subject

Statistics

Date

Jan 9, 2024

Type

docx

Pages

Uploaded by SuperHumanMouse356

1 STAT 200 Guided Exercise 3 For On-Line Students, be sure to:  Please submit your answers in a Word or PDF file to Canvas at the place you downloaded the file.  You can paste Excel/JMP output into a Word File. Please submit only one file for the assignment.  It is ok to do problems by hand. However, you will need to scan or take a picture of your work.  Guided Assignments are not graded but we check that you did the problems. Key Topics  Probability  Probability with Tables 3. An individual’s genetic makeup is determined by the genes obtained from each parent. For every genetic trait, each parent posses a gene pair; and each contributes ½ of the gene pair, with equal probabilities, to their offspring, forming a new gene pair. The offspring’s traits (eye color, baldness, etc.) come from this new gene pair, where each gene in this pair posses some characteristic. For the gene pair that determines eye color, each gene trait may be one of two types, dominant brown, (B) or recessive blue (b). A person possessing the gene pair BB or Bb has brown eyes, whereas the gene pair bb produces blue eyes. a. Suppose both parents of an individual are brown eyed, each with a gene pair Bb . What is the probability that a randomly selected child of this couple will have blue eyes? ¼ or 25% b. If one parent has brown eyes, type Bb , and the other has blue eyes, what is the probability that a randomly selected child of this couple will have blue eyes? 2/4 or 50% c. Suppose one parent is brown-eyed, type BB. What is the probability that a child has blue eyes? 0 1

2. On a standard SAT test, a typical question has five possible answers; A, B, C, D, and E. Only one answer is correct. If you guess you have a 1 out of 5 or .20% chance of being correct. a. What is the probability of not being correct on a single question if you randomly guess? 80% b. What is the probability of getting all three questions right on three questions if you you randomly guess? 8% c. What is the probability of gettting at least one question right on three questions if you randomly guess? 48.8% d. What is the probability of getting all three questions wrong on three questions if you randomly guess? 51.2% e. Training on how to do better on the SAT test advise that you should guess if you can eliminate possible answers. Suppose on a question you can eliminate two possible answers. What is the probability that you are right if you randomly guess your answer. 33.3% 3. Across the U.S. in 2020 and 2021 there was increased attention to voting security. Some states began enacting more stringent voting requirements for national elections. These requirements came with 2

controversy and debate. One requirement is identification, usually photo identification. According to the National Conference of State Legislatures (NSL), "a total of 36 states have laws requesting or requiring voters to show some form of identification at the polls, 35 of which are in force in 2020." (NSL, https://www.ncsl.org/research/elections-and-campaigns/voter-id.aspx#Laws%20in%20Effect ). The main form of photo identification for most adults in a driver’s license. However, not everyone has a driver's license, and the proportion with a license is decreasing over time. Whether you have a driver’s license depends upon a number of factors, including age, where you live, your race, and your income level, among others. I found data for those who have a license by age group in 2019. I applied this data to a pseudo survey of 1,000 adults. You can easily copy and paste this table directly into Excel and work on the questions there. Do You Have a Driver’s License? Age Yes No Total 18 to 29 170 41 211 30 to 54 377 34 411 55 to 69 220 15 235 70 and Over 117 26 143 Total 884 116 1000 a. What is the probability that a randomly selected adult in the U.S. has a driver’s license? 88.4% b. What is the probability that a randomly selected adult in the U.S. is 70 and over? 14.3% c. Given that a randomly selected adult is 18 to 29, what is the probability that he/she will not have a license? 19.43% d. Given that a randomly selected adult is 55 to 69, what is the probability that he/she will not have a license? 6.38% e. Are the events Age and Do you have a Driver’s License mutually exclusive? Explain. They are not mutually exclusive because there are people of all ages that have a driver’s license and don’t have a driver’s license. f. Are the events “55 to 69” and “Yes has a license” independent? Why? No they are not independent because the P(55 to 59) does not equal P(Yes) g. Calculate the following odds and odds ratio for Not Having a License. 3

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

(1.) Odds of Not having a license (versus Yes) for persons 18 to 29. .2412 (2.) Odds of Not having a license (versus Yes) for persons 55 to 69. . .0682 (3.) Odds ratio of (1) versus (2). Explain this in words. .2412/.0682 = 3.573 this means that people 18 to 29 are 3.5 times more likely not to have a license than people 55 to 59 4. A fast food restaurant has determined that the chance a customer will order a soft drink is .90. The chance that a customer will order a hamburger is .6, and the chance for ordering French Fries is .5. a. If a customer places an order, what is the probability that the order will include a soft drink and no fries if these two events are independent ? .45 b. The restaurant has also determined that if a customer orders a hamburger the chance the customer will also order fries is .8. Determine the probability that the order will include a hamburger and fries. .48 5. No diagnostic tests are infallible, so imagine that the probability is 0.95 that a certain test will diagnose a diabetic correctly as being diabetic, and it is 0.05 that it will diagnose a person who is not diabetic as being diabetic. It is known that roughly 10% if the population is diabetic. What is the probability that a person diagnosed as being diabetic actually is diabetic? 9500/14000=.6786 Hint: This is a use Bayes’ theorem problem, which we did not cover in the lectures. There is another way to handle this problem – make a mock 2 by 2 table of the data based on the information you already know. Once the table is complete, you can solve for the conditional probability. Since some of the probabilities are small, I would sugget you make a table that is based on 100,000 people. I have started the table for you. 4