describe an example that uses discrete probabilities or distributions. Provide an example that follows either the binomial probabilities or any discrete probability distribution, and explain why that example follows that distribution. In your responses to other students, make up numbers for the example provided by that other student, and ask a related probability question. Then show the work (or describe the technology steps) and solve that probability example.

The table lists heights (in.) of fathers and the heights (in.) of their first sons.

1. Find the linear correlation coefficient r
2. Predict the height of a father whose first son measures 77 in.

Converting P(0.15 ≤ p ≤ 0.19) to the standard normal random variable z for a sample of 500 households gives P(−1.19 ≤ z ≤ 1.19). This is the probability that a sample of 500 households will provide a sample proportion within 0.02 of the population proportion, 0.17, of households that spend more than $100 per week on groceries. Use a table to compute P(−1.19 ≤ z ≤ 1.19), rounding the result to four decimal places. P(−1.19 ≤ z ≤ 1.19) = P(z ≤ 1.19) − P(z ≤ −1.19) = 0.8830 − ???= ???

Suppose that test scores on the Graduate Management Admission Test (GMAT) are normally distributed with a mean of 530 and standard deviation of 75.

a. What GMAT score separates the highest 15% of the scores from the rest? Do not round intermediate calculations. Round your answer to the nearest whole number. GMAT score =

b. What GMAT score corresponds to the 97 percentile? Do not round intermediate calculations. Round your answer to the nearest whole number. GMAT score =

c. What GMAT score would 91% of the test takers be expected to score above? Do not round intermediate calculations. Round your answer to the nearest whole number.

GMAT score =

John wishes to study the heights of the women’s basketball team. He completes a simple random sample of women’s basketball team members. 70 71 69.25 68.5 69 70 71 70 70 69.5 74 75.5
John knows that women’s heights are normally distributed. Use the critical value method and a 5% significance level to test the claim that women’s basketball players have heights with a mean greater than 68.6 inches (population mean height of men).
1) What is the significance level ?
2) What is the critical value?
3) What is the test statistic?
4) What is the statistical conclusion? (Reject or Fail to Reject H)

A technical engineer is interested in understanding the battery life of two different laptops for student usage at a community college in California. The two models he has are Madroid and Krapple. He randomly assigned students to one of the laptop models and recorded the number of minutes the students were able to use the computer until the battery ran out. Below is the data collected.

Does the technical engineer have statistically significant evidence to present to the university budget committee to purchase Krapple because it has, on average, a longer battery life?

Provide the p-value from your analysis

You are interested in testing whether stock volatility, controlling for size and overall market returns, has an impact on returns. You conduct a regression on 89 observations, using monthly returns, specified as follows: Ri = b0 + b1 Volatilityi + b2 Sizei + b3 Rmarket + error Where Volatility is measured as standard deviation of returns in the previous month, Size is the natural log of total assets, in millions, and Rmarket is the contemporaneous market index return.

Your regression results are as follows:

The regression sum of squares is 0.12 and the residual sum of squares is 1.92.

What is the F statistic for testing whether the three independent variables are jointly statistically related to returns?

(Bonus question: is the regression statistically significant at the 5% level? Use the FDIST function to find the p-value.)

The answer should be 1.77 and the hint professor gave was "Review how to calculate the F statistic for a multiple regression." Please do the problem on excel and show all the steps. Thank you.

Pierre works five days a week. He has 12 shirts, 8 pants, 8 ties, and 4 jackets that he can wear to work. Of these, 4 shirts, 3 pants, 2 ties, and 2 jackets are blue. Each day he randomly selects one of each item to wear. Assume the selections are independent, and assume his butler launders the clothes every night so he has full closet each morning.

1. What is the probability pierres entire outfit next Monday will be blue?
2. What is the probability that Pierre will wear entirely blue outfits on Monday and Friday while wearing outfits which are not entirely blue on Tuesday through Thursday.
3. What is the probability that Pierre will wear entirely blue outfits on Monday through Friday while wearing outfits which are not entirely blue on Tuesday through Thursday?
4. What is probability Pierre will wear an entirely blue outfit on exactly 2 of the 5 days next week?

SHOW WORK

Below is collected data of the question "how many kisses have you eaten in the past day?"
This is between men and women.
The tables are these:
Male: 4, 2, 3, 1, 3, 2, 2, 0, 2, 0, 3, 1, 1, 2, 3, 5, 4  Female: 1, 2, 2, 1, 2, 4, 2, 1, 1, 3, 2, 1, 0, 1, 0, 0

Generate the experimental design using the appropriate methodology. What is the structure of the experiment?

What does the data analysis tell you?
Construct a 98% confidence interval.
Find the standard deviation.
Apply the appropriate analysis method or methods?
What type of hypothesis method will you use?
Calculate the alternate and null hypothesis and state the conclusion about who eats more kisses, men or woman.

1. Rooms in a house (Bedroom, Bathroom, Living Room, etc.) are an example of a variable that follows which scale of measurement?

            a. ratio scale

            b. interval scale

            c. nominal scale

            d. ordinal scale

2. The top 10 ranked jobs based on various criterion are listed below. Here we are interested in looking at the stress rating of each job (I picked the right one in terms of stress!...also note how many jobs that are ranked towards the top involve math and statistics!):

a. Is this data categorical or quantitative? If quantitative, is it discrete or continuous?

            b. Calculate the number of classes and class width.

            c. Construct a frequency distribution, including the classes, frequency, and relative frequency.

            d. Construct a histogram or bar graph (depending on your answer to part a), including all labels.

            e. Calculate the mean, median, and mode.

            f. Are the mean, median, and mode descriptive or inferential statistics?

            g. Calculate the range.

h. Calculate Q1.

i. Calculate Q3.

j. Calculate the IQR.

k. Find the variance.

            l. Find the standard deviation.

            m. Find the coefficient of variation.

            n. What is the 80^th percentile of this data set?

            o. Does this data set have any outliers? Use statistics in answering this question (not just your opinion).

            p. Would you use the Empirical rule or Chebyshev’s Theorem here and why?

            q. Based on the mean and median calculated above, would you expect this data to be symmetric, skewed to the left or skewed to the right and why?

           3. A survey of 900 college students resulted in the following crosstabulation regarding if they smoke or not and whether or not they drink alcohol. (2 points)

Of the students surveyed who do not smoke, what percentage also do not drink?  

1. did we underestimate the age of the gentlemen? please use the data in the spreadsheet to address this question. Use alpha = 0.01. the true age of the gentlemen is 66 years old.

65, 63, 62, 62, 67, 60, 63, 65, 65, 63, 64, 62, 55, 65, 67, 74, 71, 62, 54, 68, 65, 52, 59, 67, 75, 64, 62, 65, 56, 50, 68, 63, 62, 50, 78, 65, 62, 62, 70, 51, 65, 64, 64, 58, 72, 67, 66, 62, 67, 49, 62, 65, 53, 72, 66, 62

A.  State the Null and Alternative hypothesis (hint: should you use a one-tailed or two-tailed test here?

B. Find the critical t-values

C. Compute the t-statistic

D. make a conclusion

E. compute cohen's d.

F. compute r²

G. compute the confidence interval using alpha = 0.01

1. Assume that systolic blood pressure for adult women is normally distributed with a mean of 125.17 with a variance of 107.0. An individual woman is selected from the population. Find the following probabilities.
   1. 1. What is the probability that her systolic blood pressure is less than 125.17
   2. 2. What is the probability that her systolic blood pressure is between 112 and 140?
   3. 3. What is the probability that her systolic blood pressure will be greater than 140?

please use R and show me the code that you used? My main issue is that since not all of these are whole numbers I am a bit confused on how to plug this into R. Thanks!!

Have you ever noticed that, when you tear a fingernail, it tends to tear to the side and not down into the finger? (Actually, the latter doesn’t bear too much thinking about.). Why might this be so? One possibility is that fingernails are tougher in one direction than another. A study of the toughness of human fingernails compared the toughness of nails along a transverse dimension (side to side) compared with a longitudinal direction, with 15 measurements of each (Farren et al., 2004). The toughness of fingernails along a transerve direction averaged 3.3 kJ/m2, with a standard deviation of 0.95, while the mean toughness along the longitudinal direction was 6.2 kJ/m2, with a standard deviation of 1.48 kJ/m2. a) Test for a significant difference in the toughness of these fingernails along two dimensions. b) As it turns out, all of the fingernails in this study came from the same volunteer. Discuss what the conclusion in part (a) means. What would be required to describe the fingernail toughness of all humans?