Probability & Statistics Midterm

A sample of the manager of a sports shop's inventory finds that he sells a mean of 104 baseball caps per week, with a standard deviation of 14. What would the standard score be if 69 caps were sold in a given week?

-2.50

A box contains 5 blue marbles, 3 red and 6 white marbles. If four marbles are drawn, without replacement, what is the probability all four are red?

0

You draw three cards from a deck of 52 cards and replace the card after it is drawn. What is the probability of getting a spade, a red card abs then an ace in that order?

0.0096

The probability that De'Andre has to work overtime abs it rains is 0.028. De'Andre hears the weather forecast, and there is a 50% chance of rain. Find the probability that he will have to work overtime, given it rains.

0.056

Juniors Seniors Males 225 220 Female 210 215 If a student is selected at random, what is the probability the student is a female and a junior?

0.241

Experience-Instructors-Assistant instructors-prof. 1-5 years - 8 - 3 - 2 6-10 years -4-15-10 11-15 years -1-12-8 If a person is selected at random, what is the probability that the person is an instructor or a professor?

0.524

If the P(A)=0.33 what is the value for P(not A)?

0.670

Experience-Instructors-Assistant instructors-prof. 1-5 years - 8 - 3 - 2 6-10 years -4-15-10 11-15 years -1-12-8 If a person is selected at random, what is the probability he or she is not a professor?

0.683

The sum of all possibilities of the events in the sample space is equal to _________.

1

Find the probability of getting a number greater than 4 when a die is rolled one time

1/3

A coin is tossed 5 times. Find the probability that all 5 tosses are tails.

1/32

Fifteen students were given an arithmetic test, and the times (in minutes) to complete it were as follows. Given this is a small class, treat this data set as a population. What is the mean score for the class? 10,9,12,11,8,15,9,7,8,12,10,11,8,7,15

10.1

What is the class width of the class limits are 225-236?

12

In a 4 point grade system an A corresponds to a 4.0 points; a B corresponds to 3.0; a C corresponds to 2.0 and so forth. This semester, Christine got an A in a 4 semester-hour course, and also in a 3 semester-hour course. She got a B in a 5 semester-hour course and a C in a 2 semester-hour course. A GPA is computed as a weighted average using the number of semester hours as weights and the number of points corresponding to the grade as the data. Compute Christine's GPA for this semester.

3.36

There are 3 blue balls, 5 red balls, and 4 white balls in a bag of balls. If a person selects two of the balls, what is the probability that the second one is blue given that the first one was white?

3/11

A box contains blue chips and red chips. A person selects two chips without replacement. If the probability of selecting a blue chip and a red chip is 1/4, and the probability of selecting a blue chip on the first draw is 5/16, find the probability of selecting the red chip on the second draw, given that the first chip selected was a blue chip

4/5

Does the following data set have outliers, and if so, what are the outliers? 506,511,517,514,400,521

400

An 8 sided die, numbered 1-8, is rolled. Find the probability that the roll results in an even number or a number greater than 6.

5/8

In the Happy Hilltop Health Home, 10% of the residents play shuffleboard, 35% of the residents play poker, and 10% of the residents garden. If 5% of the residents play poker and garden, find the probability that a resident plays poker, given that they also garden.

50%

Shown below is a frequency distribution for the rise in tides at 30 selected locations in the United States. What is the average rise in tides for the 30 locations? Rise in tides (inches) Frequency 12.5-27.5 6 27.5-42.5 3 42.5-57.5 5 57.5-72.5 8 72.5-87.5 6 87.5-102.5 2

55.5

Fifteen students were given an arithmetic test, and the times (in minutes) to complete it were as follows. Given this is a small class, treat this data set as a population. Find the variance for the time it took to complete the test. 10,9,12,11,8,15,9,7,8,12,10,11,8,7,15

6.1

A sample of the manager of a sports shop's inventory finds that he sells a mean of 104 baseball caps per week, with a standard deviation of 14. Find an interval centered around the mean in which we can expect to find 75% of the data. (Think chebechyv's theorem)

76-132

A student receives test scores of 72, 75, and 81. The student's final exam score is a 78 and homework score is a 76. Each test is worth 20% of the final grade, the final exam is 25% of the final grade, and the homework grade is 15% if the final grade. What is the student's mean score in the class?

76.5

Assume you want to create a histogram for a set of data where the largest data value is 65 and the smallest data value is 14. If you were to group this data into 7 classes what should the class width be?

8.0

In a distribution of 200 values, the mean is 50 and the standard deviation is 5. Assuming the distribution is normal, what percent of your values will fall between 45 and 65?

83.85%

1000 light bulbs have an average life time of 2000 hours with a standard deviation of 25 hours. How many light bulbs are expected to last between 1925 and 2075 hours? (Multiply the percentage to the total # of light bulbs using CHEBECHYV'S THEOREM

889

In a distribution of 200 values, the mean is 50 and the standard deviation is 5. Assuming the distribution is normal, what percent of the data will fall between 40 and 60?

95%

Freshman SAT scores at the Dowd institute of technology have a sample mean of 1290 with a standard deviation of 150. What two SAT scores would I expect 95% of the freshman class to fall between?

990 and 1590

The mean score on a national engineering aptitude test is 450 and the 90th percentile is 680. A. What percent of those who took the test had scores at or above 680? B. What percent of those who took the test had scores between 450 and 680?

A. 10% B. 40%

The average grade in this test in previous years is an 86 with a standard deviation of 4. A. What is the scores for the middle 95%? B. What percent has a score more than 94? C. What percent scores between 74 and 94? D. What percent has a score more than 98?

A. 78 and 94 B. 2.5% C. 97.35% D. 0.15%

A camera store placed an ad in the newspaper showing eight digital cameras for sale. The ad says, "Our digital cameras average $155." The prices of the digital cameras are: $450,$500,$399,$155,$499,$525,$155,$490 A. Find the mean, median, and mode of the prices. Be sure to label each value B. Which measure is the store using in its ad? Why did they choose this measure? C. As a consumer, which measure would you want to see advertised? Explain

A. Mean is $396.63. Median is $470. Mode is $155 B. Mode because it is the lowest price and what occurs the most C. Mean because the prices are pretty uniform and would give me abs accurate representation of the prices of the cameras that they have in the store

The weights in pounds of the starting offensive linemen of the football teams from three high schools are as follows: Rock hill high - 170,165,140,188,195 Clover hs - 144,177,215,225,197 Fort mill hs - 166,175,196,206,219 A. Find the mean and standard deviation of the weights for three high schools (separately) B. Which team had the most variation in weights?

A. Rock hill mean - 171.6 std - 21.57 Clover mean - 191.9 std - 32.29 Fort mill mean - 192.4 std - 21.82 B. Clover

Suppose there are 200 teachers at RHHS. Mr. Ahl wants to perform a survey to find information about teachers' opinions of teaching 3 out of the 4 blocks. He comes to Honors Stats for help. A. Explain how to select 20 teachers using an SRS method. B. Explain how to select 20 teachers using Stratified random Sample. C. Explain how to use a systematic random sample to select the 20 teachers. D. He decides to stop the first 20 teachers in the parking lot. Explain why this would not be a good idea.

A. Using the SRS method, Mr. Ahl could first assign each of the 200 teachers a number. Then, he could place each of the numbers on equally sized pieces of paper into a hat. Mr. Ahl would then draw 20 names from the hat, leaving him with 20 randomly selected teachers to survey. B. Using the Stratified method, Mr. Ahl would first randomly select two buildings on campus. Then, using the list of teachers within those buildings he would randomly select 20 teachers, with 10 coming from each. To randomly select the teachers, Mr. Ahl could use the SRS method. C. Using the systematic method, Mr. Ahl would assign every 10th teacher that he came into contact with, or that entered campus, in order to select 20 teachers. D. Stopping the first 20 teachers in the parking lot would not be a good idea because it could result in bias, while also not giving every teacher a fair or equal opportunity.

The statement, "The probability that a certain sports team will win it's next game is about 60%," is an example of A) classical probability B) empirical probability C) subjective probability D) a sample space

B

Suppose the average score on a national test is 500 with a standard deviation of 100. If each score is increased by 25%, what are the new mean and standard deviation? A. 500,100 B. 525,100 C. 625,100 D. 625,105 E. 625,125

C

If a student scored 75 points in a test where the mean score was 83.5 and the standard deviation was 6.1. The students z score is ________. A. 13.69 B. 0.23 C. -0.23 D. -1.39

D

The size of the box in a box plot shows the _________ of the data set. A) difference between the mean and the median B) variance C) skewness D) interquartile range

D

Which of the five choices below describes a feature that is true about stem-and-leaf displays?

Each data value is broken into two parts

A child gets 20 heads out of 30 tosses of a coin. If he declared the chance of getting a head with that coin were 2/3, that would be an example of _____ probability

Empirical probability

T/F: Napping and exercising are not mutually exclusive events

False

T/F: When rolling two dice the sample space is 12

False

T/F: when determining probability of an event all possible answers can range from zero to hundred

False

T/F: when the outcome of event A does not affect the probability of the outcome of a subsequent event B, then the events are said to be dependent

False

When two events are independent, the probability of both occurring is:

P(A and B) = P(A) x P(B)

Select the most appropriate term from the choices below. This tool for visually organizing data identifies the frequency or relative frequency of events or categories in decreasing order or occurrence

Pareto chart

This tool for visually organizing quantitative data is useful for detecting patterns abs extreme values by organizing and grouping the data, but allows one to recover the original data if desired.

Stem and leaf plot

Which describes a feature that is true about bar graphs?

The bars in the graph can be vertical or horizontal

Which describes a feature that is true about histograms?

The bars in the graph touch

Which describes a feature that is true about time plots?

The intervals on the horizontal axis represent equal units of time

Schools in York County want to add a special tax to the ballet to increase teacher pay. They survey residentswith the following question: "Would you support a special tax that will cost taxpayers 50 million over the next 20years to raise teacher pay?" What is the potential source of bias? Explain.

The potential source of bias is Wording bias because it favors one side. The question that they survey residents with shows how much money it will cost the taxpayers, thus favoring the salary of the teacher over the taxpayer.

Identify sampling method and one possible source of bias In a recent report, a group of scientists claimed that Americans are consuming an excessive amount of selenium in their diets. The National Science Foundation has stated that the safe upper limit is 200 micrograms per day. In order to determine the extent of the problem in Plano, researchers divided the town into five regions based on economic levels and drew random samples of households from each region. They then interviewed an adult at the residence and measured their daily consumption of selenium.

The sampling method is stratified because after the researchers divided the town into five regions, they drew random samples from households within each region. The information provided above does not suggest that they drew samples from each household in each region, but that they randomly sampled households from each region. Therefore, the sampling method must be stratified. One possible source of bias in this study would be selenium. The daily consumption of selenium presents a wording bias because many adult residence that were surveyed may not understand where selenium comes from in your diet, or may not even know what that is. Another possible source of bias could be Response, because people may not answer truthfully, as they feel pressured to answer as if they eat healthily, when they may in fact have an unhealthy diet.

what's the difference between observational study and an experiment?

When researchers perform an observational study, they are simply observing as the term suggests. They are not providing any treatments or changing any variables. On the other hand, in an experiment, treatments are imposed and different variables may be changed in order to get results.

which of the following(s) are important in the design of experiments? a. control of potential confounding (extraneous) b. randomization in assigning subjects to different treatments c. replication of the experiment using sufficient numbers of subjects

a, b, & c

Tell what types of bias is possible with each scenario. Voluntary, Response, NonResponse, Wording, or Convenience. (Make sure you give me 4 answers) a. Mr. Vo ask the opinion of the first five students that enter into the classroom. b. Mr. Vo hands each student a survey and ask them to fill it in. He receives 3 surveys back. c. Mr. Vo puts surveys out on the front table. 15 students pick up the survey, fills it out and turns it in. d. Mr. Vo is asked to fill out a survey about his recent hospital visit. The questions include medical terminology that he is unable to pronounce and are not too sure what they mean.

a. The type of bias for this scenario would be Convenience bias because there is no system to which Mr. Vo is receiving this information. It is simply based on chance. b. The type of bias for this scenario is NonResponse bias. Although Mr. Vo hands each student a survey, all but 3 decide to not take part. Additionally, three survey responses would leave him with inadequate results. c. The type of bias for this scenario would be Voluntary bias because 15 students chose to take part in the survey, and were not forced to. d. The type of bias for this scenario is Wording because the questions include terms that Mr. Vo does not understand. As a result, this will affect his answers.

A firm tested the durability of four different types of tires by having 4 Toyotas each randomly equipped with one of the types of tires. In similar fashion, 4 Hondas were used, each randomly equipped with one of the tires type. In a like manner, 4 Ford were each randomly outfitted with one of the four tire brands. Then each of the twelve cars ran over a test track until the tires showed signs of serious wear. At that point the average mileage of the three cars using one type of tire was compared to the average mileage of the three cars using the second type of tires, and so on. This design is:

an example of randomized block design

Which of the following is an area where statistics is used? a) gambling b) insurance c) all of them d) medicine

c

DETERMINE THE BEST METHOD OF DATA COLLECTION a study of the salaries of all of the college professors at winthrop university

census

a researcher wants to determine what percent of first graders still believe in the tooth fairy. he decides to use ms. wilson's first graders at independence elementary as his sample. the sampling technique being used by the researcher is: (hint: there are 3 1st graders)

cluster

Which of the following is an area of inferential statistics? a) organizing data b) collecting data c) generalizing from populations to samples d) generalizing from samples to populations

d

CLASSIFY AS INFERENTIAL OR DESCRIPTIVE STATISTICS during the memorial day weekend, 20 people were killed in car accidents

descriptive

CLASSIFY AS INFERENTIAL OR DESCRIPTIVE STATISTICS of the 30 nurses in pediatrics, 20 work during the day and 10 work at night

descriptive

the collection, organization, summarization, and presentation of data is called _____________.

descriptive statistics

T/F: Hypothesis testing is the highest level of measurement

false

T/F: Statistics is divided into two main areas called descriptive and hypothetical statistics

false

T/F: the subject matter that a college professor teaches would be an example of ordinal level of data

false

CLASSIFY AS INFERENTIAL OR DESCRIPTIVE STATISTICS based on past figures, it is predicted that only 52% of registered voters will vote in the next election

inferential

CLASSIFY AS NOMINAL, ORDINAL, INTERVAL, OR RATIO LEVEL DATA SAT scores at rhhs

interval

CLASSIFY AS NOMINAL, ORDINAL, INTERVAL, OR RATIO LEVEL DATA the hair color of student athletes

nominal

What is the level of measurement that consists of classifying data into mutually exclusive categories in which no order or ranking can be imposed?

nominal level

CLASSIFY AS NOMINAL, ORDINAL, INTERVAL, OR RATIO LEVEL DATA gold, silver, and bronze metals at the olympics

ordinal

a parameter is a characteristic or measure obtained by using all the data values for a ________

population

CLASSIFY AS QUANTITATIVE OR QUALITATIVE the favorite flavors of ice cream for first graders

qualitative

CLASSIFY AS QUANTITATIVE OR QUALITATIVE the religious affiliation of students at rock hill high school

qualitative

a person's blood type would be an example of what type of data?

qualitative

CLASSIFY AS QUANTITATIVE OR QUALITATIVE the number of pages typed by a secretary

quantitative

CLASSIFY THE SAMPLING TECHNIQUE AS RANDOM, SYSTEMATIC, STRATIFIED, CLUSTER, OR CONVENIENCE mrs. lawrence wants to do a survey on how many freshman at her school have tried drugs. there are 300 freshmen at her school, so she assigns each student a number, puts them in a box, shakes them up, and draws 40 different numbers

random

DETERMINE THE BEST METHOD OF DATA COLLECTION a study of 100 members of a larger labor union were polled regarding a proposed new contract

sampling

DETERMINE THE BEST METHOD OF DATA COLLECTION a study where you would like to determine the chance of getting three girls in a family of three children (think on the terms of probability)

simulation

A company with offices in five different countries is interested in estimating proportion of its employees in favor of banning smoking on the office premises. It is known that the views of people from different countries on issues like smoking tend to vary due to the influence of different social structures. Which of the following is an appropriate sampling technique to use in this situation and why? (Hint: Mr. Vo is fluent in both Vietnamese and English, yet he lives in the U.S)

stratified sample, because the population is divided into five strata- namely the five offices in the five different countries

CLASSIFY THE SAMPLING TECHNIQUE AS RANDOM, SYSTEMATIC, STRATIFIED, CLUSTER, OR CONVENIENCE a reporter interviews every 4th person

systematic

samantha wants to poll her classmates on their favorite Netflix show. she puts her classmates' names in alphabetical order and then picks every third name. what is samantha's sampling technique called?

systematic

T/F: one way to obtain a random sample is to use random numbers

true

T/F: the variable "gender" would be an example of a qualitative variable

true

What are the stems for the data set 62,71,67,53,66,35,34,45?

{3,4,5,6,7}