Math 15 midterm
3.9 Disjoint vs. independent: In parts (a) and (b), identify whether the events are disjoint, independent, or neither (events cannot be both disjoint and independent).a) You and a randomly selected student from your class both earn A's in this course.
independent neither false
Below is a table that gives the mean and standard deviation for an administration of the SAT and ACT exams. Both tests follow a nearly normal distribution and as such we can model then using the normal distribution. Figure 4.4 SAT ACT Mean 1500 21 SD 300 5 If Sam scores a 1450 on the SAT, will his Z-score be positive of negative?
negative
b) The university gym opens at 9 am on Saturday mornings. One Saturday morning at 8:55 am there are 27 students outside the gym waiting for it to open. Should you use the same approach from part (a) to calculate the expected number of smokers among these 27 students?
no these 27 students are not a random sample from the students population
Another article titled The School Bully Is Sleepy states the following:"The University of Michigan study, collected survey data from parents on each child's sleep habits and asked both parents and teachers to assess behavioral concerns. About a third of the students studied were identified by parents or teachers as having problems with disruptive behavior or bullying. The researchers found that children who had behavioral issues and those who were identified as bullies were twice as likely to have shown symptoms of sleep disorders."A friend of yours who read the article says, "The study shows that sleep disorders lead to bullying in school children." Is this statement justified? If not, how best can you describe the conclusion that can be drawn from this study?
no this is an observation
Reading the paper: Below are excerpts from two articles published in the NY Times a) An article tiled:Risks: Smokers Found More Prone to Dementiastates the following:"Researchers analyzed data from 23,123 health plan members who participated in a voluntary exam and health behavior survey from 1978 to 1985, when they were 50-60 years old. 23 years later, about 25% of the group had dementia, including 1,136 with Alzheimer's disease and 416 with vascular dementia. After adjusting for other factors, the researchers concluded that pack-a-day smokers were 37% more likely than nonsmokers to develop dementia, and the risks went up with increased smoking; 44% for one to two packs a day; and twice the risk for more than two packs."Based on this study, can we conclude that smoking causes dementia later in life? Explain your reasoning.
no this is observation
1.38 City council survey: A city council has requested a household survey be conducted in a suburban area of their city. The area is broken into many distinct and unique neighborhoods, some including large homes, some with only apartments, and others a diverse mixture of housing structures. Identify the sampling methods described below, and comment on whether or not you think they would be effective in this setting. a) Randomly sample 50 households from the city
simple Random, Effective
Studies are often done by pharmaceutical companies to determine the effectiveness of a treatment program. Suppose that a new AIDS antibody drug is currently under study. It is given to patients once the AIDS symptoms have revealed themselves. Of interest is the average (mean) length of time in months patients live once they start the treatment. A researcher follows a set of 20 patients with AIDS from the start of treatment until their deaths. The following data (in months) are collected.3; 4; 11; 15; 16; 17; 22; 44; 37; 16; 14; 24; 25; 15; 26; 27; 33; 29; 35; 44In this setting, the average time to death for the 20 patients is a
statistic
The histogram and box plots below show the distribution of finishing times for male and female winners of the New York Marathon between 1970 and 1999. What may be the reason for the bimodal distribution? Explain. Your Answer:
the bimodal distribution has 2 peaks this shows the bimodal distribution
A smooth curve that represents a probability density function (also called a density or distribution), has a special property: the total area under the density's curve is 1.
true
NORMAL DISTRIBUTION FACTS Many variables are nearly normal, but none are exactly normal. Thus the normal distribution, while not perfect for any single problem, is very useful for a variety of problems. We will use it in data exploration and to solve important problems in statistic
true
RANDOM VARIABLEA random process or variable with a numerical outcome.
true
The binomial distribution is used to describe the number of successes in a fixed number of trials.
true
The four conditions to check for a binomial distribution are: (1) The trials are independent. (2) The number of trials, n, is fixed. (3) Each trial outcome can be classified as a success or failure. (4) The probability of a success, p, is the same for each trial.
true
(a) What percent of the data fall between Q1 and the median? (b) What percent is between the median and Q3? (c) What percent is between Q1 and Q3?
(a) 25% (b) 25% (c) 50%
What proportion of scores in a normal distribution fall between: (a) plus or minus 1 standard deviation of the mean (b) plus or minus 2 standard deviations of the mean (c) plus or minus 3 standard deviations of the mean
(a) 68% (b) 95% (d) 99.7%
Below are the final scores of 20 introductory statistics students. 79, 83, 57, 82, 94, 83, 72, 74, 73, 71, 66, 89, 78, 81, 78, 81, 88, 69, 77, 79 Give the (a) Mean, (b) Standard Deviation, (c) Median (d) IQR
(a) 77.70 (b) 8.44 (c) 78.50 (d) 10
(a) In your own words explain what is meant by �0:Independence Model and ��:Alternative Model. (b) Also, give what it means for the data to support �0 and for the data to support ��. Note: This is not machine graded. Your Answer:
(a) Ho: Independence Model refers to a statistical hypothesis in which two variables are considered to be independent of each other, meaning that the value of one variable does not affect the value of the other variable. Ha: Alternative Model refers to a statistical hypothesis that contradicts the null hypothesis (Ho) and suggests that there is a relationship or dependence between the two variables being studied. (b) For the data to support Ho, the results of the statistical test performed should not reject the null hypothesis and show no evidence of a relationship between the two variables being studied. For the data to support Ha, the results of the statistical test performed should reject the null hypothesis and provide evidence of a relationship or dependence between the two variables being studied.
Give the short-hand for a normal distribution with (a) mean 5 and standard deviation 3,(b) mean -100 and standard deviation 10, and(c) mean 2 and standard deviation 9.
(a) N(�=5,�=3) (b) N(�=−100,�=10) (c) N(�=2,�=9)
About 9% of people are left-handed. Suppose 2 people are selected at random from the U.S. population. Because the sample size of 2 is very small relative to the population, it is reasonable to assume these two people are independent. (a) What is the probability that both are left-handed? (b) What is the probability that both are right-handed? Assume that the number of ambidextrous people is negligible.
(a) P(Both Left Handed) = 0.0081 (b) P(Both Right Handed) = 0.8281
The probability of rolling the sum of two fair dice is given below. Let A represent the event where we roll two dice and their total is less than 12. (a) What does the event Ac represent? (b) Determine P(Ac) from Figure above. (c) Determine P(A).
(a) The complement of A: when the total is equal to 12. (b) 1/36 (c) 35/36
question 2 on week 2 Use the plots in below figure to compare the incomes for counties across the two groups.
(a) The gain data had an increase in median income as compared to the no gain data, (b) The gain data has more variability than the no gain. (c) Yes, they are both skewed right (d) There are one mode for each group
(a) Which is more affected by extreme observations, the mean or median? (b) Is the standard deviation or IQR more affected by extreme observations?
(a) The mean (b) The Standard Deviation
4.44 Heights of 10 year olds: Heights of 10 year olds, regardless of gender, closely follow a normal distribution with mean 55 inches and standard deviation 6 inches.
(a) What is the probability that a randomly chosen 10 year old is shorter than 48 inches?0.1210 (b) What is the probability that a randomly chosen 10 year old is between 60 and 65 inches?0.1558 (c) If the tallest 10% of the class is considered "very tall", what is the height cutoff for "very tall"?62.68 inches (d) The height requirement for Batman the Ride at Six Flags Magic Mountain is 54 inches. What proportion of 10 year olds cannot go on this ride?0.4325
4.36 Speeding on the I-5, Part I: The distribution of passenger vehicle speeds traveling on the Interstate 5 Freeway (I-5) in California is nearly normal with a mean of 72.6 miles/hour and a standard deviation of 4.78 miles/hour.
(a) What percent of passenger vehicles travel slower than 80 miles/hour? 93.94 % ( (b) What percent of passenger vehicles travel between 60 and 80 miles/hour?93.53 % (c) How fast do the fastest 5% of passenger vehicles travel? 80.46 mph (d) The speed limit on this stretch of the I-5 is 70 miles/hour. Approximate what percentage of the passenger vehicles travel above the speed limit on this stretch of the I-5.70.54
4.8 CAPM: The Capital Asset Pricing Model (CAPM) is a financial model that assumes returns on a portfolio are normally distributed. Suppose a portfolio has an average annual return of 14.7% (i.e. an average gain of 14.7%) with a standard deviation of 33%. A return of 0% means the value of the portfolio doesn't change, a negative return means that the portfolio loses money, and a positive return means that the portfolio gains money
(a) What percent of years does this portfolio lose money, i.e. have a return less than 0%?32.8% (b) What is the cutoff for the highest 15% of annual returns with this portfolio?48.9012%
Two US adults are randomly selected from the given distribution. The shaded region represents the probability that a single adult is between 180 and 185 cm which is 0.1157. What is the probability that the two adults selected are between 180 and 185 cm tall?
0.0134
Three US adults are randomly selected. The probability a single adult is between 180 and 185 cm is 0.1157 What is the probability that all three are between 180 and 185 cm tall?
0.1157 × 0.1157 × 0.1157 = 0.0015
According to the National Center for Health Statistics, the heights of males in the USA closely follow a normal distribution with mean 69.2 inches and standard deviation 2.8 inches. What is the probability that a randomly selected male from the USA will be shorter than 66.4 inches? That is P(X < 66.4) = ?
0.16
GPAs at College of the Redwoods are normally distributed with a mean of 2.14 and a standard deviation of 0.5. Find the �-score for a GPA of 2.33.
0.3600
Below is a table that gives the mean and standard deviation for an administration of the SAT and ACT exams. Both tests follow a nearly normal distribution and as such we can model then using the normal distribution. Figure 4.4 SATACT Mean 1500 21 SD 300 5 Tomas scores a 24 on the ACT. What is his Z-score?
0.6
According to the National Center for Health Statistics, the heights of males in the USA closely follow a normal distribution with mean 69.2 inches and standard deviation 2.8 inches. What is the probability that a randomly chosen male from the USA is between 63.6 and 74.8 inches?
0.954
Below is a table that gives the mean and standard deviation for an administration of the SAT and ACT exams. Both tests follow a nearly normal distribution and as such we can model then using the normal distribution. Figure 4.4 SAT ACT Mean1500 21 SD 300 5 Zora scores 1850 on the SAT. What is her Z-score?
1.17
The bookstore also offers a chemistry textbook for $159 and a book supplement for $41. From past experience, they know about 25% of chemistry students just buy the textbook while 60% buy both the textbook and supplement. What proportion of students don't buy either book? Assume no students buy the supplement without the textbook.
100% -25% - 60% = 15% of students do not buy any books for the class.
The game of roulette involves spinning a wheel with 38 slots: 18 red, 18 black, and 2 green. A ball is spun onto the wheel and will eventually land in a slot, where each slot has an equal chance of capturing the ball. You watch a roulette wheel spin 3 consecutive times and the ball lands on a red slot each time. What is the probability that the ball will land on a red slot on the next spin?
18/38
Two books are assigned for a chemistry class: a textbook and its corresponding study guide. The bookstore determined 30% of enrolled students do not buy either book, 45% buy the textbook only, and 25% buy both books, and these percentages are relatively constant from one term to another. If there are 200 students enrolled, how many books (both textbook and study guide) should the bookstore expect to sell to this class?
190
Suppose weights of the checked baggage of airline passengers follow a nearly normal distribution with mean 20 kilograms and standard deviation 2.5 kilograms. Most airlines charge a fee for baggage that weigh in excess of 25 kilograms. Determine what percent of airline passengers incur this fee.
2.3%
Two books are assigned for a chemistry class: a textbook and its corresponding study guide. The bookstore determined 30% of enrolled students do not buy either book, 45% buy the textbook only, and 25% buy both books, and these percentages are relatively constant from one term to another. The textbook for this chemistry class costs $130 and the study guide $43. How much revenue should the bookstore expect from this class of 200 students
20.350
Below is a table that gives the mean and standard deviation for an administration of the SAT and ACT exams. Both tests follow a nearly normal distribution and as such we can model then using the normal distribution. Figure 4.4 SAT ACT Mean1500 21 SD 300 5 If Sam scores a 1450 on the SAT, what proportion of people scored higher than Sam
56.62
According to the National Center for Health Statistics, the heights of males in the USA closely follow a normal distribution with mean 69.2 inches and standard deviation 2.8 inches. If the tallest (top) 10% of males in the USA are considered "very tall", what is the height cutoff for "verytall"?
72.8
Below are a histogram and a normal probability plot for the heights of 25 randomly selected female college students. Do these data appear to follow a normal distribution? Explain your reasoning using the graphs provided.
???
Divide the city into neighborhoods, randomly sample 10 neighborhoods, and sample all households from those neighborhoods
Cluster, Ineffective
Sample the 200 households closest to the city council offices
Convenience, Ineffective
What can you see in a dot plot that you cannot see in a histogram?
Counts (frequency) for an individual value.
Question 11. Means, Medians, Standard Deviations, and IQRs: Answer the following about each dataset. (Round to two decimal places where appropriate)
Dataset I: 0105060100 a) The median of Dataset I is:50 b) Using Rguroo, the IQR of Dataset I is from 10-20 c) The mean of Dataset I is:44 d) The standard deviation of Dataset I is: 40.37 Dataset II: 01005006001000 e) The median of Dataset II is: 500 f) Using Rguroo, the IQR of Dataset II is from 100-600 g) The mean of Dataset II is: 440 h) The standard deviation of Dataset II is: 403.73
Question 10. Means, Medians, Standard Deviations, and IQRs: Answer the following about each dataset. (Round to two decimal places where appropriate)
Dataset I: 12345 a) The median of Dataset I is: 3 b) Using Rguroo, the IQR of Dataset I is from 2-4 c) The mean of Dataset I is: 3 d) The standard deviation of Dataset I is: 1.58 Dataset II: 678910 e) The median of Dataset II is: 8 f) Using Rguroo, the IQR of Dataset II is from 7-9 g) The mean of Dataset II is: 8 h) The standard deviation of Dataset II is: 1.58
2.2 Associations: Describe the relationship between the predictor and response variables in each of the four scatterplots below.
Describe plot (1) above: Positive, linear b) Describe plot (2) above: No association Correct c) Describe plot (3) above: Positive, non-linear d) Describe plot (4) above: Negative, linear
Two books are assigned for a statistics class: a textbook and its corresponding study guide. The university bookstore determined 20% of enrolled students do not buy either book, 55% buy the textbook only, and 25% buy both books, and these percentages are relatively constant from one term to another. If there are 100 students enrolled, then around 20 students will not buy either book (0 books total), about 55 will buy one book (55 books total), and approximately 25 will buy two books (totaling 50 books for these 25 students). The bookstore should expect to sell about 105 books for this class. Would you be surprised if the bookstore sold slightly more or less than 105 books and why?
If they sell a little more or a little less, this should not be a surprise. Recall that there is natural variability in observed data. For example, if we would flip a coin 100 times, it will not usually come up heads exactly half the time, but it will probably be close.
The histogram and box plots below show the distribution of finishing times for male and female winners of the New York Marathon between 1970 and 1999. What features are apparent in the box plot but not in the histogram?
In the box plot the more extreme observations, many of which could be considered outliers, are easier to identify.
On page 30, the concept of shape of a distribution was introduced. A good description of the shape of a distribution should include modality and whether the distribution is symmetric or skewed to one side. Using Figure 1.25 as an example, explain why such a description is important.
Just giving summary statistics will fail to give the entire story. The three distributions are quite different in shape and yet all have the same mean and standard deviation
Estimate the median for the 400 observations shown in the histogram, and note whether you expect the mean to be higher or lower than the median.
Median = (80+85)/2 = 82.5 The distribution is skewed to the left. therefore, the mean is expected to be lower than the median.
Divide the city into neighborhoods, randomly sample 10 neighborhoods, and then randomly sample 20 households from those neighborhoods
Multistage, Ineffective
A recent article in a college newspaper stated that college students get an average of 5.5 hrs of sleep each night. A student who was skeptical about this value decided to conduct a survey by randomly sampling 25 students. On average, the sampled students slept 6.25 hours per night. Identify which value represents the sample mean and which value represents the claimed population mean.
Population mean = 5.5. Sample mean = 6.25.
Given the following scatterplots, which plot shows a nonlinear positive association?
Scatterplot 3
What do scatterplots reveal about the data, and how might they be useful?
Scatterplots are helpful in quickly spotting associations relating variables, whether those associations come in the form of simple trends or whether those relationships are more complex.
In a class of 25 students, 24 of them took an exam in class and 1 student took a make-up exam the following day. The professor graded the first batch of 24 exams and found an average score of 74 points with a standard deviation of 8.9 points. The student who took the make-up the following day scored 64 points on the exam. Does the new student's score increase or decrease the average score?
Since the new score is smaller than the mean of the 24 previous scores, the new mean should be smaller than the old mean.
Scores on stats final: (This questioin is based on the materialo covered in LAB 3) Below are final exam scores of 20 Introductory Statistics students. 5766697172737477787879798181828383888994 a) The mean score is 77.7 points and the standard deviation is 8.44 points. Do the exam scores approximately follow the 68-95-99.7% Rule? How can you decide?
Since the percentage is close to the 68-95-99.7 rule I would say yes. byes the data follows a normal distribution because I see the histogram in this graph is symmetric and normal probability plot does show a Straightline.
Divide the city into neighborhoods, then sample 20 households from each neighborhood
Stratified, Effective
Here, we exam the relationship between homeownership, which for the loans data can take a value of rent, mortgage (owns but has a mortgage), or own, and app_type, which indicates whether the loan application was made with a partner (joint) or whether it was an individual application. Consider the following contingency table: What does the 0.906 represent in Figure 2.21?
The 0.906 represents the fraction of applicants that rent who applied as individuals.
In a class of 25 students, 24 of them took an exam in class and 1 student took a make-up exam the following day. The professor graded the first batch of 24 exams and found an average score of 74 points with a standard deviation of 8.9 points. The student who took the make-up the following day scored 64 points on the exam. Does the new student's score increase or decrease the standard deviation of the scores?
The new score is more than 1 standard deviation away from the previous mean, and this will tend to increase the standard deviation of the data.
The below figure suggests three distributions for household income in the United States. Only one is correct. Which one must it be? What is wrong with the other two?
The probabilities of (a) do not sum to 1. The second probability in (b) is negative. This leaves (c), which sure enough satisfies the requirements of a distribution. One of the three was said to be the actual distribution of US household incomes, so it must be (c).
2.5 Parameters and statistics: Identify which value represents the sample mean and which value represents the claimed population mean. a) American households spent an average of about $61 in 2007 on Halloween merchandise such as costumes, decorations and candy. To see if this number had changed, researchers conducted a new survey in 2008 before industry numbers were reported. The survey included 2150 households and found that average Halloween spending was $52 per household.
The sample mean is 52 dollars, while the claimed population mean is 61 dollars. bb) The average GPA of students in 2001 at a private university was 3.45. A survey on a sample of 260 students from this university yielded an average GPA of 3.52 in Spring semester of 2012. The sample mean is 3.52 and the claimed population mean is 3.45
Consider the following contingency table: fig 2.29 Is this an observational study or an experiment? What implications does the study type have on what can be inferred from the results?
The study is an experiment, as patients were randomly assigned an experiment group. Since this is an experiment, the results can be used to evaluate a causal relationship between the malaria vaccine and whether patients showed signs of an infection.
Take a look at the dot plot below Can you see the skew in the data and if so, what type of skew is it?
There is skew in the distribution and it appears to be skewed right.
Light and exam performance: A study is designed to test the effect of light level on exam performance of students. The researcher believes that light levels might have different effects on males and females, so wants to make sure both are equally represented in each treatment. The treatments are fluorescent overhead lighting, yellow overhead lighting, no overhead lighting (only desk lamps). a) What is the response variable?
What is the response variable?exam performance b) What is the explanatory variable? light level c) What are the levels of the explanatory variable?fluorescent overhead lighting yellow overhead lighting, no overhead lighting (only desk lamps). d) What is the blocking variable?sex e) What are the levels of the blocking variable?male and female
Describe the distribution in the histograms below and match them to the box plots.
a . 2 b 3 c 1
4.2 Area under the curve, Part II: Find the probability of each of the following, if Z~N(μ = 0,σ = 1).(please round any numerical answers to 4 decimal places)a)
a P(Z > -1.13) =0.8708 b) P(Z < 0.18) =05714 c) P(Z > 8) =0 d) P(| Z | < 0.5) =0.3829
The graph of a normal distribution is shaped like
a bell
2.27 Make-up exam: In a class of 25 students, 24 of them took an exam in class and 1 student took a make-up exam the following day. The professor graded the first batch of 24 exams and found an average score of 84 points with a standard deviation of 6.2 points. The student who took the make-up the following day scored 65 points on the exam.
a decreased b the new average is 83.24 c increased
question 12 Distributions and appropriate statistics (Part II): For each of the following, state whether you expect the distribution to be symmetric, right skewed, or left skewed. Also specify whether the mean or median would best represent a typical observation in the data, and whether the variability of observations would be best represented using the standard deviation or IQR. Explain your reasoning.(a) Housing prices in a country where 25% of the houses cost below $350,000, 50% of the houses cost below $450,000, 75% of the houses cost below $1,000,000 and there are a meaningful number of houses that cost more than $6,000,000.The distribution is expected to be: (b) Housing prices in a country where 25% of the houses cost below $300,000, 50% of the houses cost below $600,000, 75% of the houses cost below $900,000 and very few houses that cost more than $1,200,000.The distribution is expected to be:
a skewd right b median c IQR d symmetric e mean f standar deviation g right skewed h median I IRQ j Right skewed K median L IRQ
3.29 College smokers: At a university, 13% of students smoke.
a) Calculate the expected number of smokers in a random sample of 100 students from this university: 13
Income and gender: The relative frequency table below displays the distribution of annual total personal income (in 2009 inflation-adjusted dollars) for a representative sample of 96,420,486 Americans. These data come from the American Community Survey for 2005-2009. This sample is comprised of 59% males and 41% females.
a) Describe the distribution of total personal income: 35000 to 49000 b) What is the probability that a randomly chosen US resident makes less than $50,000 per year? 62.20 % (please round to two decimal places, ie. xx.xx%) c) What is the probability that a randomly chosen US resident makes less than $50,000 per year and is female? 25.50 % d) The same data source indicates that 71.8% of females make less than $50,000 per year. What could explain the discrepancy between this number and the number you calculated in part c)? not valid it indicates that 71.8% of 41% of females make less than $50000 per year.71.8% of 41% = 29.438%which is not equal in part (C). so it is not valid
4.5 GRE scores, Part II: Assume that scores on the verbal portion of the GRE (Graduate Record Exam) follow the normal distribution with mean score 151 and standard deviation 7 points, while the quantitative portion of the exam has scores following the normal distribution with mean 153 and standard deviation 7.67. Use this information to answer the following:
a) Find the score of a student who scored in the 80th percentile on the Quantitative Reasoning section of the exam. 159.46 b)Find the score of a student who scored worse than 70% of the test takers in the Verbal Reasoning section of the exam. 147.33
4.1 Area under the curve, Part I: Find the probability of each of the following, if Z~N(μ = 0,σ = 1).(please round any numerical answers to 4 decimal places)
a) P(Z < -1.35) = 0.0885 b) P(Z > 1.48) =0.694 c) P(-0.4 < Z < 1.5) =0.5886 d) P(| Z | >2) =0.0456
Means, Medians, Standard Deviations, and IQRs: Answer the following about each dataset. (Round to two decimal places where appropriate) Dataset I: 12345
a) The median of Dataset I is: 3 b) Using Rguroo, the IQR of Dataset I is from 2 and 4 c) The mean of Dataset I is: 3 d) The standard deviation of Dataset I is: 1.58
Means, Medians, Standard Deviations, and IQRs: Answer the following about each dataset. (Round to two decimal places where appropriate)
a) The median of Dataset I is: 6 b) Using Rguroo, the IQR of Dataset I is from 5 7 c) The mean of Dataset I is: 6 d) The standard deviation of Dataset I is: 2.24 Dataset II: 356720 e) The median of Dataset II is: 6 f) Using Rguroo, the IQR of Dataset II is from 5 7 g) The mean of Dataset II is: 8.2 h) The standard deviation of Dataset II is: 6.76
question 8 Means, Medians, Standard Deviations, and IQRs: Answer the following about each dataset. (Round to two decimal places where appropriate) Dataset I: 35679
a) The median of Dataset I is: 6 b) Using Rguroo, the IQR of Dataset I is from 5 7 c) The mean of Dataset I is: 6 d) The standard deviation of Dataset I is: 2.24 Dataset II: 356720 e) The median of Dataset II is: 6 f) Using Rguroo, the IQR of Dataset II is from 5 and 7 g The mean of Dataset II is: 8.2 h) The standard deviation of Dataset II is: Correct 6.76
question 9 Means, Medians, Standard Deviations, and IQRs: Answer the following about each dataset. (Round to two decimal places where appropriate) Dataset I: 35679
a) The median of Dataset I is: 6 b) Using Rguroo, the IQR of Dataset I is from 5-7 c) The mean of Dataset I is: 6 d) The standard deviation of Dataset I is: 2.24 Dataset II: 35879 e) The median of Dataset II is: 7 f) Using Rguroo, the IQR of Dataset II is from 5-8 g) The mean of Dataset II is: 6.4 h) The standard deviation of Dataset II is: 2.41
2.6 Sleeping in college: A recent article in a college newspaper stated that college students get an average of 7 hrs of sleep each night. A student who was skeptical about this value decided to conduct a survey by randomly sampling 26 students. On average, the sampled students slept 6.8 hours per night. Identify which value represents the sample mean and which value represents the claimed population mean.
a) What is the sample mean? 6.8 hours b) What is the claimed population mean?7hours
3.6 Dice Rolls: If you roll a pair of fair dice, what is the probability of each of the following? (round all answers to 4 decimal places)
a) getting a sum of 1?0.000 b) getting a sum of 5?0.1111 c) getting a sum of 12?0.0278
3.5 Coin Flips: If you flip a fair coin 10 times, what is the probability of each of the following?(please round all answers to 4 decimal places)
a) getting all tails?0.0010 b) getting all heads?0.0010 c) getting at least one tails?0.9990
4.7 LA weather, Part I: The average daily high temperature in June in LA is 76°F with a standard deviation of 5°F. Suppose that the temperatures in June closely follow a normal distribution.
a. 0.0359 b 69.59225
4.6 Triathlon times, Part II: In Exercise 3.4 we saw two distributions for triathlon times: N(μ=4351,σ=578) for Men, Ages 30 - 34 and N(μ=5216,σ=808)for the Women, Ages 25 - 29 group. Times are listed in seconds. Use this information to compute each of the following:
a. 3400.2767 b 6251.4924
