There are 10 marbles in a jar. They are identical except for color. Four are Red, three are Blue, two are Yellow and one is White. You draw a marble from the jar, note its color, and set it aside. Then, you draw another marble from the jar and note its color.

a) What is the probability that you draw two Red marbles?

b) What is the probability that you draw a Blue marble GIVEN that you have drawn a Red one?

c) What is the probability that you draw a Blue and a Yellow marble in EITHER ORDER?

d) What is the probability that EITHER marble you draw is White?

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The following data represent the weight of a child riding a bike and the rolling distance achieved after going down a hill without pedaling.  

Find the 95% prediction interval for rolling distance when a child riding the bike weighs 106 lbs. (round to 4 decimal places

Statistics Canada did a survey of Canadians in 2018 and determined that the average adult female over the age of 18 watches 25.6 hours of television per week while the average male watches 20.9 hours per week. Suppose that the sample comprised 35 females and 50 males (obviously the real samples were much larger) and that the sample standard deviations were 7.2 hours for females and 7 hours for males.

a) [4 marks] Is there sufficient evidence, at the 5% significance level, to show that adult women spend more time watching TV than adult men? Assume equal variances and a pooled standard deviation of 7.08.

b) [2 marks] Calculate the appropriate confidence interval to confirm the conclusion from part a). Does this confidence interval confirm your conclusion from part (a)? Explain.

c) [2 marks] Suppose you were more concerned with detecting a real difference than worrying about attributing a difference when there is none. In this case, would a significance level of 0.10 or 0.01 be more appropriate?

a) Given X ~N(10, 18)  and n = 64

P(13 < X < 14) =

b)

Given X ~N(10, 18)  and n = 64

x-bar ~ N(10, _________)

c) Given X ~N(10, 18)  and n = 64

μ = _____

Question 2 – Social Responsibility of Business The Nobel prize winning “monetarist” economist Milton Friedman made a famous but very controversial assertion that “the social responsibility of business is to increase its profits”. Corporate social responsibility has become a hot topic of discussion, and an independent research group has claimed that at least 54% of Canadians agree with the Friedman assertion. You take a random sample of 125 people and find only 57 agreeing with the Friedman assertion.

a) Test whether the random sample constitutes sufficient evidence to disprove the research group's claim. Use the p-value approach and a 5% level of significance.

b) Calculate the appropriate one-sided 95% confidence interval. How would you use this interval to complete the test above?

c) Suppose you want to estimate the proportion of Canadians who agree with the Friedman assertion, using a margin of error of ± 2% for a 95% two-sided confidence interval. What sample size would be required?

Hi I'm having a hard time understand this can someone please explain it to me? Thank you.

Cholesterol is a type of fat found in the blood. It is measured as a concentration: the number of milligrams of cholesterol
found per deciliter of blood (mg/dL). A high level of total cholesterol in the bloodstream increases risk for heart disease.
For this problem, assume cholesterol in men and women follows a normal distribution, and that “adult man” and “adult
woman” refers to a man/woman in the U.S. over age 20. For adult men, total cholesterol has a mean of 188 mg/dL and a
standard deviation of 43 mg/dL. For adult women, total cholesterol has a mean of 193 mg/dL and a standard deviation
of 42 mg/dL. The CDC defines “high cholesterol” as having total cholesterol of 240 mg/dL or higher, “borderline high” as
having a total cholesterol of more than 200 but less than 240, and “healthy” as having total cholesterol of 200 or less. A
study published in 2017 indicated that about 11.3% of adult men and 13.2% of adult women have high cholesterol.

1) The CDC guidelines for cholesterol health are applied to both men and women, but men and women have different
distributions of total cholesterol.
a. What approximate percent of women have a total cholesterol that would be considered “healthy?” (For this
problem, give your answer as a percent, not a decimal. Round your answer to one decimal place.)
b. What approximate percent of men have a total cholesterol that would be considered “healthy?” (For this
problem, give your answer as a percent, not a decimal. Round your answer to one decimal place.)

2) A group of 256 randomly chosen adult men is selected. How many of them do you expect to have a total cholesterol of less than 200 mg/dL? (Round your answer to one decimal place.)

3) Oatmeal is a food that is high in fiber and low in fat. A dietician says, “People who regularly eat oatmeal tend to have
lower cholesterol.” A group of 121 randomly selected adult women who regularly eat oatmeal has a sample mean
total cholesterol of 185 mg/dL.
a. What is the probability a randomly selected group of adult women has a sample mean total cholesterol of 185
or less?
b. Would this be a significant result? (Choose one.)
A. Yes B. No C. Not enough information

Some job applicants are required to have several interviews before a decision is made. The number of required interviews and the corresponding probabilities are: 1 (0.09); 2 (0.31); 3 (0.37); 4 (0.12); 5 (0.05); 6 (0.05).

a) Does this information describe a probability distribution? What is the sum of probabilities?

b) Assuming it does, find its mean and standard deviation.

c) Use the range rule of thumb to identify the range of values for usual numbers of interviews.

d) Is it unusual to have a decision after just one interview? Explain.

Suppose a friend of yours is hosting a wine tasting. His wine supply includes three different types of deluxe wine. All bottles come from the same winery and all wines were harvested in 2017. He currently owns 7 bottles of chardonnay, 9 bottles of shiraz, and 13 bottles of champagne. Throughout the wine tasting, your friend will only open a new bottle of wine when there are no other bottles of wine open at the time.

1. Create a tree diagram of the sample space and label all events and their corresponding 
probabilities.


 2. What is the probability that all bottles in the wine tasting are of the same type of wine?

Allegiant Airlines charges a mean base fare of $86. In addition, the airline charges for making a reservation on its website, checking bags, and inflight beverages. These additional charges average $35 per passenger. Suppose a random sample of 50 passengers is taken to determine the total cost of their flight on Allegiant Airlines. The population standard deviation of total flight cost is known to be $36. Use z-table.

a. What is the population mean cost per flight?
$

b. What is the probability the sample mean will be within $10 of the population mean cost per flight (to 4 decimals)?

c. What is the probability the sample mean will be within $5 of the population mean cost per flight (to 4 decimals)?

Construct a​ 95% confidence interval to estimate the population proportion using the data below.    

x equals 23, n equals 80, N equals 500

The​ 95% confidence interval for the population proportion is left parenthesis nothing comma nothing right parenthesis . ​(Round to three decimal places as​ needed.)

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 63 ounces and a standard deviation of 5 ounces. Use the Standard Deviation Rule, also known as the Empirical Rule.

a) 99.7% of the widget weights lie between _____ and _____

b) What percentage of the widget weights lie between 53 and 78 ounces? %

c) What percentage of the widget weights lie below 68 ?

At one college, the proportion of students that needed to go into debt to buy their supplies each term (books, tech, etc.) was once known to be 74%. An SRS of 60 students was then surveyed in a later term, in order to see if this previous proportion would still be supported by the new sample evidence.

Out of these 60 sampled students, 52 needed to go into debt to buy their supplies that term. Using a normal distribution of approximation (according to the CLT): We will conduct a two-sided significance test at a 3% significance level, to see if our sample has produced statistically significant evidence.

1. State the hypotheses (both the null and alternative) for this two-sided significance test.

2. Using N(μ, σ) normal distribution notation: Identify the very specific normal distribution (by stating the exact numerical values for μ and σ within this notation) that should be used to perform this test.

3. Find the percent P-value from this test.

The manager of The Cheesecake Factory in Boston reports that on six randomly selected weekdays, the number of customers served was 120, 130, 100, 205, 185, and 220. She believes that the number of customers served on weekdays follows a normal distribution.

Construct the lower bound of the 90% confidence interval for the average number of customers served on weekdays. (Round the sample standard deviation to 2 decimal places, the "t" value to 3 decimal places, and the final answer to 2 decimal places.)

The mean number of sick days an employee takes per year is believed to be about 10. Members of a personnel department do not believe this figure. They randomly survey 8 employees. The number of sick days they took for the past year are as follows: 10; 6; 14; 4; 10; 9; 8; 9. Let X = the number of sick days they took for the past year. Should the personnel team believe that the mean number is about 10? Conduct a hypothesis test at the 5% level.

Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your answers to three decimal places.)

Noonan syndrome is a genetic condition that can affect the heart, growth, blood clotting, and mental and physical development. Noonan et al. examined the stature of men and women with Noonan syndrome. The study contained 29 male and 44 female adults. One of the cut-off values used to assess the stature was the third percentile of adult height. 24 of the females fell below the third percentile of female adult height and 11 of the males fell below the third percentile of adult male height.

a) Present the information and the data given in the problem in a 2 x 2 contingency table format.

b) What are the two categorical variables involved in this study?

c) Can the two categorical variables involved in this study be tested for independence (no association)? Why or why not?

d) Can the proportion of males who fall below their respective third percentile adult height and the proportion of females who fall below their respective third percentile adult height be tested for their homogeneity ? Why or why not?