The distribution of the number of people in line at a grocery store has a mean of 3 and a variance of 9. A sample of the numbers of people in line in 50 stores is taken.

(a) Calculate the probability that the sample mean is more than 4? Round values to four decimal places.

(b) Calculate the probability the sample mean is less than 2.5. Round answers to four decimal places.

(c) Calculate the probability that the the sample mean differs from the population mean by less than 0.5. Round answers to four decimal places.

Please help, and show step by step. Thank you.

question 12:

The risk of a portfolio can be lower than the risk of the two individual components that make up the portfolio when

Question 1:
From past experience, we know that there are 14% of freshmen, 25% of sophomores, 32% of juniors and the remaining are seniors at NAU. We also know that 21% of the freshmen, 22% of the sophomore and 11% of the juniors have taken BA 201. Also 86% of the general student population at NAU have not taken BA 201. If we randomly ask a student from NAU and find out that she has NOT taken BA201, what is the probability (in percentage) that she is a freshman? Use Excel to solve. Hint: (1) Use Excel to setup the joint probability table; (2) Notice that 21%, 22% and 11% are the conditional probabilities NOT joint probabilities; (3) just enter the value without the % sign in the answer box.

Question 2:

When two events are collectively exhaustive and mutually exclusive, which of the following are always true? (2 correct answers)

Question 4:

When there are only two possible events A and B that are mutually exclusive, which of the following is(are) always true? (2 correct answers)

Question 5:

When there are more than two events and they are statistically independent, which of the following is(are) always true? (2 correct answers)

Pete's Power Pizzas sells a chocolate/tofu filled pastry. Pete's currently sells this pastry for $13.15, and makes it for a variable cost of $5.35 per pie. A drop in cocoa prices will reduce variable cost for this product by $0.52 per pie. Pete's is thinking of reducing the pie's selling price by $0.94. By what percent must Quantity demanded increase so that Pete's just maintains its current total contribution margin (margin per unit times units sold)? (Report your answer as a percent. Report 25.5%, for example, as "25.5". Rounding: tenth of a percent.) The answer is 5.7. Please show all work to get to the answer of 5.7.

Assume you were asked to interview a researcher about the merits and weaknesses of quasi-experimental designs. Critically discuss the merits and weakness of a single group time series design

Also include in the answer the following questions with references:

1. What are the merits of each of the specific designs?
   
2. When should you use each of the specific designs?
   
3. What is the statistical analysis that is used for each of the specific designs?
   
4. What are the limitations of each of the specific designs?
   
5. What is one research question for each of the specific designs (using a topic area that you are interested in)?

In 2012, the General Social Survey asked a random sample of adults, "Compared to most people, how informed are you about politics?" Suppose that the following are the data classified by their responses to this question and their age group (the data has been modified slightly for testing purposes):

Carry out a chi-square test. Test H0: there is no relationship between age and how politically informed the person is versus Ha: there is a relationship between age and how politically informed the person is. Use α=0.01. χ2(±0.0001)= ______

P(±0.0001)= _______

a) There is no a relationship between age and how politically informed the person is

b) There is a relationship between age and how politically informed the person is

A group of 20 people have a Russian roulette party. Each person at the party plays (pulls the trigger) three times.

In between the times they re-spin the barrel. What is a box model for the fraction of people who survive the party? What is the expected value and standard error?

If they do not re-spin the barrel, what is a box model for the fraction of survivors? What is the expected value and standard error?

A consensus forecast is the average of a large number of individual analysts' forecasts. Suppose the individual forecasts for a particular interest rate are normally distributed with a mean of 6 percent and a standard deviation of 1.6 percent. A single analyst is randomly selected. Find the probability that his/her forecast is

Round your answers to 4 decimal places.

(a) At least 3.4 percent.

(b) At most 8 percent.

(c) Between 3.4 percent and 8 percent.

Listed below are the lead concentrations in ug/g measured in different traditional medicines. Use a 0.05 significance level to test the claim that the mean lead concentration for all such medicines is less than 14 ug/g.

​17.5         3.5            12.5         9                4                9.5            20.5         10             10.5         21

1. Thirty years ago, the mean number of rides that were disabled (broken) for more than two

hours at Disneyland was 10.2 per month. The current CEO, Bob Iger, believes that number has

gone down and randomly selects 11 months from the past three years and checks on the number

of disabled rides. If the mean has decreased, he will give the members of the maintenance staff a

$50K bonus this year. If not, they will all be immediately fired.

14

10

5

6

8

10

10

8

9

9

7

a. At the 10% significance level, do the data provide evidence that the mean number of disabled

rides per month has decreased?

b. In the context of this problem, describe Type I and Type II errors and their consequences.

Which one, in your opinion, is more severe?

Type I:

Type II:

You are given data from a company that recently laid off a large number of workers. The data includes the following variables:

Age of the employee

Number of years of education

Marital status (1=married/0=single)

Number of years that the employee worked for the company

Was a manager (1=yes/0=no)

Was in sales (1=yes/0=no)

Was primary earner in the family (1=yes/0=no)

95% confidence interval for proportion of employees who were in sales before they were laid off.

What do the confidence intervals tell you about the typical employee who got laid off?

Are low-fat diets or low-carb diets more effective for weight loss? A simple random sample of 85 adults went on a low-carbohydrate diet for 6 months. At the end of that time, the average weight loss was 4.8 kilograms with a standard deviation 6.04 kilograms. A second simple random sample of 77 adults went on a low-fat diet. Their average weightloss was 4 kilograms with a standard deviation of 5.08 kilograms. Can you conclude that the true mean weightloss differs between the two diets? Use a 10% significance to decide. Group 1: Low-Carb Group 2: Low-Fat Round to the fourth Select the correct alternative sign: μ 1 μ 2 Test Statistic: p-value: Decision Rule: Did Significance Happen? There enough evidence to conclude

A genetic experiment involving peas yielded one sample of offspring consisting of 443 green peas and 120 yellow peas. Use a 0.05 significance level to test the claim that under the same​circumstances, 26​% of offspring peas will be yellow. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, conclusion about the null​ hypothesis, and final conclusion that addresses the original claim. Use the​ P-value method and the normal distribution as an approximation to the binomial distribution. What are the null and alternative​ hypotheses?

1. State the research hypothesis (non-directional) and the null hypothesis. Make sure you include both DV and IV in the hypotheses from #1 above

2.According to the post-hoc results table, which pairs of the cottages do show the statistically significant difference in “Number of traumas experienced” (e.g. “Cottage A vs. B”)?

do you think that Pill and Mark had good reasons fo choosing the research topic initially ?

Let X be a random variable such that P(X = 1) = 0.4 and P(X = 0) = 0.6.  Compute Var(X).