A random variable is normally distributed. It has a mean of 245 and a standard deviation of 21. I just need G.

a.)If you take a sample of size 10, can you say what the shape of the distribution for the sample mean is? Why?

b.) For a sample of size 10, state the mean of the sample mean and the standard deviation of the sample mean.

c.) For a sample of size 10, find the probability that the sample mean is more than 241.

d.) If you take a sample of size 35, can you say what the shape of the distribution of the sample mean is? Why?

e.) For a sample of size 35, state the mean of the sample mean and the standard deviation of the sample mean.

f.) For a sample of size 35, find the probability that the sample mean is more than 241.

g.) Compare your answers in part c and f. Why is one smaller than the other?

Pre-Employment Drug Screening Results are shown in the following Table:

If 1 of the 200 test subjects is randomly selected, find the probability that the subject had a positive test result, given that the subject actually uses drugs. That is,

(positive test result subject uses drugs).

If 1 of the 200 test subjects is randomly selected, find the probability that the subject actually uses drugs, given that he or she had a positive test result. That is,

(subject uses drugs ).

The mean per capita income is 15,654 dollars per annum with a standard deviation of 570

dollars per annum.

What is the probability that the sample mean would differ from the true mean by less than  63 dollars if a sample of 315 persons is randomly selected? Round your answer to four decimal places.

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. What is the value of the test statistic for this hypothesis test?

Question 2. What is the P-value for this hypothesis test?

A researcher wants to estimate the difference in the means of two populations. A random sample of 36 items from the first population results in a sample mean of 430. A random sample of 49 items from the second population results in a sample mean of 460. The population standard deviations are 120 for the first population and 140 for the second population. From this information, a 95% confidence interval for the difference in population means is _______.

Select one:

a. -102.83 to 42.43

b. -27.6049 to 87.6049

c. -76.53 to 16.53

d. -95.90 to 35.90

The U.S. Energy Information Administration (US EIA) reported that the average price for a gallon of regular gasoline is $3.95 . The US EIA updates its estimates of average gas prices on a weekly basis. Assume the standard deviation is $.24 for the price of a gallon of regular gasoline and recommend the appropriate sample size for the US EIA to use if they wish to report each of the following margins of error at 95%confidence. Round up to the next whole number.

a. The desired margin of error is $.09 The appropriate sample size is ____ .

b. The desired margin of error is $.06 The appropriate sample size is ____ .

c. The desired margin of error is $.05 The appropriate sample size is ____.

1. You randomly select 36 restaurants and measure the temperature of coffee sold at each. The sample mean temperature is 162.0°F. Temperatures historically have had a population standard deviation of 10.0°F. Which of the following intervals is the correct 95% confidence interval for the true mean? (T interval or Z interval)

2. If all other quantities remain the same, how does the indicated change affect the width of a confidence interval? Decrease the level of confidence from 95% to 90%?

A researcher is interested in determining if the attitude about homosexual marriages is dependent on region. In order to do the Chi-Square association test, she ran analysis with Minitab and came up with the contingency table that summarizes the actual observations and the expected observations. α=0.05.

Report your test statistic and your conclusion .

Round your test statistic to the nearest decimal. Report your conclusion as D (dependent) or I (independent)

A random rearrangement doe not separate out between repeated letters. Consider word CHRISTMASTIME.

a) What's the expected # vowels in first three letters of random rearrangement of CHRISTMASTIME?

b) What's probability that all the S's happen before all the I's in random rearrangement of CHRISTMASTIME?

c) What's probability that word CHRIST happens in consecutive letters of uniform rearrangement of CHRISTMASTIME?

Anderson et al. (1990) studied the effect of diet on the level of low-density lipoprotein (LDL, the “bad” cholesterol) for a group of men with hypercholesterolemia. Half the subjects were given a diet that included corn flakes and the other half were given a diet that included oat bran. LDL was then measured after two weeks. Subjects were then crossed-over to the alternative diet for an additional two weeks. LDL was measured again. The LDL measurements are shown below. Test the null hypothesis that the mean difference in LDL points to a population in which the difference is zero, suggesting that the one diet is no better than the other for controlling LDL. What does the result suggest? (this can be answered in one or two sentences)

LDL (in mmol/L) -------- Corn Flakes 4.61 6.42 5.40 4.54 3.98 3.82 5.01 4.34 3.80 4.56 5.35 3.89

Oat Brab 3.84 5.57 5.85 4.80 3.68 2.96 4.41 3.72 3.49 3.84 5.26 3.73 -----------------------

I can't figure out how to create the decision tree with the sending a messaged situation!

The crew of Endurance can visit two planets (Mann’s and Edmunds’). They can choose to visit neither planets, one of the two planets, or both planets. The characteristics of Mann’s planet are below:

• 30% chance of finding a perfectly habitable planet

• can support all of Earth’s current population if it is

• can support none of Earth’s population if it is not

And the characteristics of Edmunds’ planet are below:

• 50% chance of finding a perfectly habitable planet

• can support 50% of Earth’s current population if it is (because it is not as large as Mann’s planet)

• can support 20% of Earth’s current population if it is not (because it is still partially habitable)

The crew also needs to decide when to send a message to Earth to let them know which planet to migrate to. The possible outcomes for the different time steps of when they send that message are below:

• If they send the message before visiting both planets, none of the Earth’s population would have perished on Earth before receiving that message.

• If they send the message after visiting only one planet (either one), 10% of the Earth’s population would have perished on Earth before receiving that message.

• If they send the message after visiting both planets, 25% of the Earth’s population would have perished on Earth before receiving that message.

What should the crew do to save as many of Earth’s population as possible? Specifically, which planet or planets should they visit, if any and in what order, and when should they send the message to Earth? Draw a decision tree to solve this problem.

There are 9 balls out of which one ball is heavy in weight and rest are of the same weight. In how many occurrences will you find the heavy ball?

4. The director of the Wisconsin Department of Business Licensing is looking for ways to improve employee productivity. Specifically, she would like to see an improvement in the percentage of applications that employees process correctly. The director randomly selects 50 employees and gather data on the percentage of applications each one correctly processed last month. On the recommendation of a consultant, the director has these 50 employees complete a 3-day workshop on Proactive Synergy Restructuring Techniques. At the end of the month following the training, the director collects the application processing data for the same 50 employees. Help the director analyze these data by conducting a hypothesis test. From a statistical point of view, what can you tell the director?

The Heinlein and Krampf Brokerage firm has just been instructed by one of its clients to invest $250,000 of her money obtained recently through the sale of land holdings in Ohio. The client has a good deal of trust in the investment house, but she also has her own ideas about the distribution of the funds being invested. In particular, she requests that the firm select what- ever stocks and bonds they believe are well rated but within the following guidelines:

● Municipal bonds should constitute at least 20% of the investment.

● At least 40% of the funds should be placed in a combination of electronic firms, aerospace firms, and drug manufacturers.

● No more than 50% of the amount invested in municipal bonds should be placed in a high-risk, high-yield nursing home stock.

Subject to these restraints, the client’s goal is to maximize projected return on investments. The analysts at Heinlein and Krampf, aware of these guidelines, prepare a list of high-quality stocks and bonds and their corresponding rates of return:

(a) Formulate this portfolio selection problem using LP.

(b) Solve this problem.