The semester average grade for a statistics course is 76 with a standard deviation of 5.5. Assume that stats grades have a bell-shaped distribution and use the empirical rule to answer the following questions (explain your responses with the help of a graph):

1. What is the probability of a student’s stat grade being greater than 87?

2. What percentage of students has stat grades between 70.5 and 81.5?

3. What percentage of students has stat grades between 70.5 and 65?

4. What is the probability of a student’s stat grade being greater than the mean?

Questions 15 –17

Personal incomes in a city have an average of $80,000 and standard deviation of $20,000.

15. The percent of personal incomes over $100,000 is

(a) 0.05 (b) 0.1 (c) 0.1587 (d) 0.1841 (e) Not enough information to calculate.

16. In a random sample of 100 people, the probability that the average income in the sample is over $82,000 is

(a) 0.05 (b) 0.1   (c) 0.1587 (d) 0.1841 (e) Not enough information to calculate.

17. In another random sample of 400 people, the probability that the average income in this sample is at least $3,000 more than the sample average income in Question 16 is

(a) 0.03 (b) 0.05 (c) 0.07 (d) 0.09 (e) Not enough information to calculate.

The time needed to complete a final examination in a particular college course is normally distributed with a mean of 100 minutes and a standard deviation of 20 minutes. Answer the following questions.

(a) What is the probability of completing the exam in one hour or less?

(b) What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes?

(c) Assume that the class has 90 students and that the examination period is 130 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time?

An article in the New England Journal of Medicine described a randomized experiment that investigated the effectiveness of two medications for nausea in patients undergoing chemotherapy treatments for cancer. In the experiment, 157 patients were divided at random into two groups. One group of 78 patients were given a standard anti-nausea drug called prochlorperazine, while the other group of 79 patients received delta-9-tetrahydrocannabinol (i.e., THC, the active ingredient in marijuana). Both medications were delivered orally and no patients were told which of the two drugs they were taking. The observed response was whether or not the patient experienced relief from nausea when undergoing chemotherapy. 16 of the patients taking prochlorperazine experienced relief from nausea, while 36 of the patients taking THC experienced relief from nausea. Conduct a significance test to determine if there is evidence that there is a difference in the effectiveness of the two drugs

In San Francisco, 15% of workers take public transportation daily.

A) In a sample of 20 San Fransisco workers what is the probability that between 9 and 10 workers take public transportation daily?

B) In a sample of 19 San Fransisco workers what is the probability that at most 5 workers take public transportation daily?

C) In a sample of 19 San Fransisco workers what is the probability that at least 14 workers take public transportation daily?

D) In a sample of 15 San Fransisco workers what is the expected number of workers who take public transportation daily?

E) In a sample of 15 San Fransisco workers what is the variance of the number of workers who take public transportation daily?

A particular type of ballpoint pen uses minute ball bearings that are targeted to
have a diameter of 0.5 mm. The lower and upper speci cation limits under which the
ball bearing can operate are 0.49 mm (lower) and 0.51 mm (upper). Past experience
has indicated that the ball bearings are approximately normally distributed with a
mean of 0.503 mm and a standard deviation of 0.004 mm. If you select a sample of 25
ball bearings, what is the probability that the sample mean is:
(a) between the target and the population mean of 0.503 mm?
(b) between the lower speci cation limit and the target?
(c) above the upper speci cation?
(d) The probability is 93.32% that the sample mean diameter will be above what value?

How can one design a future sampling study to have a lower bound? How could more information be used?

1 point) According to data from the Tobacco Institute Testing Laboratory, a certain brand of cigarette contains an average of 1.4 milligrams of nicotine. An advocacy group questions this figure, and commissions an independent test to see if the the mean nicotine content is higher than the industry laboratory claims.
The test involved randomly selecting ?=15n=15 cigarettes, measuring the nicotine content (in milligrams) of each cigarette. The data is given below.

1.7,1.6,1.8,2.0,1.4,1.4,1.9,1.6,1.3,1.5,1.2,1.4,1.7,1.2,1.51.7,1.6,1.8,2.0,1.4,1.4,1.9,1.6,1.3,1.5,1.2,1.4,1.7,1.2,1.5

(a) Do the data follow an approximately Normal distribution? Use alpha = 0.05.   ? yes no  

(b) Determine the ?P-value for this Normality test, to three decimal places.
?=P=

(c) Choose the correct statistical hypotheses.
A. ?0:?⎯⎯⎯⎯⎯=1.4,??:?⎯⎯⎯⎯⎯≠1.4H0:X¯=1.4,HA:X¯≠1.4
B. ?0:?⎯⎯⎯⎯⎯>1.4,??:?⎯⎯⎯⎯⎯<1.4H0:X¯>1.4,HA:X¯<1.4
C. ?0:?⎯⎯⎯⎯⎯=1.4,??:?⎯⎯⎯⎯⎯<1.4H0:X¯=1.4,HA:X¯<1.4
D. ?0:?=1.4,??:?≠1.4H0:μ=1.4,HA:μ≠1.4
E. ?0:?>1.4,??:?<1.4H0:μ>1.4,HA:μ<1.4
F. ?0:?=1.4??:?>1.4H0:μ=1.4HA:μ>1.4


(d) Determine the value of the test statistic for this test, use two decimals in your answer.
Test Statistic =

(e Determine the ?P-value for this test, to three decimal places.
?=P=

(f) Based on the above calculations, we should  ? reject not reject  the null hypothesis. Use alpha = 0.05

side note: these are checkboxes so multiple answers can be chosen

In what everyday applications might some of the geometric problems discussed above (such as finding the volume of a frustum of a pyramid) be useful?

A. Trading

B. The temples called ziggurats

C. System of canals for irrigation

D. Eating

Data collected by an arcade store manager yielded the following confidence interval for the proportion of customers who played the new video game the store just bought: (21% to 30%). Give the margin of error in percentage points

he motion picture industry is a competitive business. More than 50 studios produce several hundred new motion pictures each year, and the financial success of the motion pictures varies considerably. The opening weekend gross sales, the total gross sales, the number of theaters the movie was shown in, and the number of weeks the motion picture was in release are common variables used to measure the success of a motion picture. Data on the top 100 grossing motion pictures released in 2011 (Box Office Mojo website, March 17, 2012) are contained in a file named 2011Movies. Table 3.10 below shows the data for the first 10 motion pictures in this file. Note that some movies, such as War Horse, were released late in 2011 and continued to run in 2012. Use the numerical methods of descriptive statistics presented in this chapter to learn how these variables contribute to the success of a motion picture. Include the following in your report: 1. Descriptive statistics for each of the four variables along with a discussion of what the descriptive statistics tell us about the motion picture industry. 2. What motion pictures, if any, should be considered high-performance outliers? Explain. 3. Descriptive statistics showing the relationship between total gross sales and each of the other variables. Discuss. Opening Gross Sales Number Weeks Total Gross Sales of in (Smillions) ($millions) Theaters Release Motion Picture Harry Potter and the Deathly 169.19 381.01 4375 19 Hallows Part 2 Transformers: Dark of the Moon The Twilight Saga: Breaking 97.85 138.12 352.39 281.29 4088 4066 15 Dawn Part The Hangover Part II Pirates of the Caribbean: On 85.95 90.15 254.46 241.07 3675 4164 16 19 Stranger Tides Fast Five Mission: Impossible-Ghost 86.20 12.79 209.84 208.55 3793 3555 15 13 Protocol Cars 2 Sherlock Holmes: A Game of 66.14 39.64 191.45 186.59 4115 3703 25 13 Shadows Thor 65.72 181.03 3963 16

The presence of student-owned information and communication technologies (smartphones, laptops, tablets, etc.) in today's college classroom creates learning problems when students distract themselves during lectures by texting and using social media. Research on multitasking presents clear evidence that human information processing is insufficient for attending to multiple stimuli and for performing simultaneous tasks.

To collect data on how multitasking with these technologies interferes with the learning process, a carefully-designed study was conducted at a mostly residential large public university in the Northeast United States. Junco, R. In-class multitasking and academic performance. Computers in Human Behavior (2012)

At the beginning of a semester a group of students who were US residents admitted through the regular admissions process and who were taking the same courses were selected based on their high use of social media and the similarities of their college GPA's. The selected students were randomly assigned to one of 2 groups:

group 1 students were told to text and use Facebook during classes in their usual high-frequency manner;

group 2 students were told to refrain from any use of texting and Facebook during classes.

At the conclusion of the semester the semester GPA's of the students were collected. The results are shown in the table below.

IN-CLASS MUTLITASKING STUDY

Frequent Facebook Use and Texting   

x₁ = 2.87

s₁ = 0.67

n₁ = 65

No Facebook Use or Texting

x₂ = 3.16

s₂ = 0.53

n₂ = 65

Do texting and Facebook use during class have a negative affect on GPA? To answer this question perform a hypothesis test with
H₀: μ₁−μ₂ = 0
where μ₁ is the mean semester GPA of all students who text and use Facebook frequently during class and μ₂ is the mean semester GPA of all students who do not text or use Facebook during class.

Question 1. Calculate a 95% confidence interval for μ1−μ2 where μ₁ is the mean semester GPA of all students who text and use Facebook frequently during class and μ₂ is the mean semester GPA of all students who do not text or use Facebook during class.

A. A stress analysis was conducted on random samples of epoxy-bonded joints from two species of wood. A random sample of 120 joints from species A had a mean shear stress of 1250 psi and a standard deviation of 350 psi, and a random sample of 90 joints from species B had a mean shear stress of 1400 psi and a standard deviation of 250 psi. (i) Conduct a hypothesis test with α = 0.02 to determine whether or not there is a difference between the mean sheer stress of the two species of wood. Be sure to state your hypotheses, test statistic, p-value, and conclusions. (ii) Construct a 98% two-sided confidence interval for the difference µA − µB. Compare the CI with the results of the hypothesis test in (i). Are the conclusions consistent

Bernard Haldane Associates conducted a survey in March 2004 of 1021 workers who held white-collar jobs but who had changed jobs in the previous twelve months. Of these workers, 56% of the men and 35% of the women were paid more in their new positions when they changed jobs. Suppose that these percentages are based on random samples of 510 men and 511 women white-collar workers.

1. Construct a 95% confidence interval for the difference between the two population proportions.

__________________

2. Using the 2% significance level, can you conclude that the two population proportions are different? Use the p-value approach.