he Iowa Energy are scheduled to play against the Maine Red Claws in an upcoming game in the National Basketball Association (NBA) G League. Because a player in the NBA G League is still developing his skills, the number of points he scores in a game can vary substantially. Assume that each player’s point production can be represented as an integer uniform random variable with the ranges provided in the following table: Player lowa Energy Maine Red Claws 1     [5,20]     [7,12] 2     [7,20]     [15,20] 3     [5,10]     [10,20] 4     [10,40]     [15,30] 5     [6,20]     [5,10] 6     [3,10]     [1,20] 7     [2,5]     [1,4] 8     [2,4]     [2,4] Develop a spreadsheet model that simulates the points scored by each team and the difference in their point totals. (a) What are the average and standard deviation of points scored by the Iowa Energy? Round your answers to one decimal place. Average: Standard Deviation: What is the shape of the distribution of points scored by the Iowa Energy? (b) What are the average and standard deviation of points scored by the Maine Red Claws? Round your answers to one decimal place. Average: Standard Deviation: What is the shape of the distribution of points scored by the Maine Red Claws? (c) Let Point Differential = Iowa Energy points – Maine Red Claw points. What is the average Point Differential between the Iowa Energy and Maine Red Claws? What is the standard deviation of the Point Differential? If your answer is negative, enter a minus sign in the input box. Round your answers to one decimal place. Average: Standard Deviation: What is the shape of the Point Differential distribution? (d) What is the probability that the Iowa Energy scores more points than the Maine Red Claws? Round your answer to the nearest whole number. % (e) The coach of the Iowa Energy feels that they are the underdog and is considering a riskier game strategy. The effect of this strategy is that the range of each Energy player’s point production increases symmetrically so that the new range is [0, original upper bound + original lower bound]. For example, Energy player 1’s range with the risky strategy is [0, 25]. How does the new strategy affect the average and standard deviation of the Energy point total? How does that affect the probability of the Iowa Energy scoring more points than the Maine Red Claws? Round first two numerical answers to one decimal place and the last answer to a whole percentage. The average Iowa Energy point total is relatively unchanged at points, and the standard deviation of the Energy point total points. The probability of the Iowa Energy scoring more points than the Maine Red Claws %.

The Iowa Energy are scheduled to play against the Maine Red Claws in an upcoming game in the National Basketball Association (NBA) G League. Because a player in the NBA G League is still developing his skills, the number of points he scores in a game can vary substantially. Assume that each player’s point production can be represented as an integer uniform random variable with the ranges provided in the following table: Player lowa Energy Maine Red Claws 1     [5,20]     [7,12] 2     [7,20]     [15,20] 3     [5,10]     [10,20] 4     [10,40]     [15,30] 5     [6,20]     [5,10] 6     [3,10]     [1,20] 7     [2,5]     [1,4] 8     [2,4]     [2,4] Develop a spreadsheet model that simulates the points scored by each team and the difference in their point totals. (a) What are the average and standard deviation of points scored by the Iowa Energy? Round your answers to one decimal place. Average: Standard Deviation: What is the shape of the distribution of points scored by the Iowa Energy? (b) What are the average and standard deviation of points scored by the Maine Red Claws? Round your answers to one decimal place. Average: Standard Deviation: What is the shape of the distribution of points scored by the Maine Red Claws? (c) Let Point Differential = Iowa Energy points – Maine Red Claw points. What is the average Point Differential between the Iowa Energy and Maine Red Claws? What is the standard deviation of the Point Differential? If your answer is negative, enter a minus sign in the input box. Round your answers to one decimal place. Average: Standard Deviation: What is the shape of the Point Differential distribution? (d) What is the probability that the Iowa Energy scores more points than the Maine Red Claws? Round your answer to the nearest whole number. % (e) The coach of the Iowa Energy feels that they are the underdog and is considering a riskier game strategy. The effect of this strategy is that the range of each Energy player’s point production increases symmetrically so that the new range is [0, original upper bound 1 original lower bound]. For example, Energy player 1’s range with the risky strategy is [0, 25]. How does the new strategy affect the average and standard deviation of the Energy point total? How does that affect the probability of the Iowa Energy scoring more points than the Maine Red Claws? Round first two numerical answers to one decimal place and the last answer to a whole percentage. The average Iowa Energy point total is relatively unchanged at points, and the standard deviation of the Energy point total points. The probability of the Iowa Energy scoring more points than the Maine Red Claws %.

Suppose you measure the number of "success" outcomes n out of N binary (success/failure) trials (e.g. your local oracle predicts tomorrow's weather on N different occasions and you assess the number of correct predictions n). From this sample you determine the proportion p=n/N of the success outcomes. Clearly, we are dealing here with a sample of size N from i.i.d. Bernoulli processes X, and p is an estimator for the underlying probability of success in each Bernoulli trial.

How do we put a confidence interval on the proportion p? In other words, suppose we have a particular sample of N Bernoulli (binary) trials and we compute p=0.58. Is the difference from a random coin toss (which would be p=0.5) significant? Can we calculate a 95% confidence interval, so that we could tell that true underlying proportion (success probability) is likely bounded by, say, [0.48,0.63]?

This is a well known problem and a solution is very easy to find on the internet (you are welcome to use any external resources). However, it is important to not only have the formula but also be able to explain how things work. In particular, this is what I am looking for: an explanation of how things work. Specifically, think about the following:

·        p is a function of the sample drawn, so it is a random variable. How is it distributed (at least as N becomes large), and why? [Hint: represent failure as 0, and success as 1]. What is the distribution of p at any sample size N?

·        What parameter of the estimator's distribution determines the width of the confidence interval and what is the value of that parameter for N Bernoulli trials [Hint: we can easily calculate the variance of a single Bernoulli random variable with values 0,1 and success probability p: the (true!) mean, e.g. the expectation, is μ=0*(1-p)+1*p=p; hence the variance is σ=(1-p)*(0-p)^2+p*(1-p)^2=(1-p)*p^2+(1-p)^2*p=p*(1-p)*(p+1-p)=p*(1-p). What will happen in N trials? You can consult the derivation of the standard error of the mean]

·        Now that we have the estimator p, and we know shape and width of its distribution, how do we form the confidence interval at e.g. 80% confidence level? 90%? Use normal (not t-distribution) as it is what's usually used in conjunction with proportion estimates.

1) The distribution of the amount of money spent by college students for school supplies in a semester is normally distributed with a mean of $275 and a standard deviation of $20.

Using the Standard Deviation Rule, there is a 99.7% probability that students spent between:

Group of answer choices

$255 and $295

$215 and $315

$235 and $315

$235 and $335

$215 and $335

2) The distribution of the amount of money spent by college students for school supplies in a semester is normally distributed with a mean of $275 and a standard deviation of $20.

Using the Standard Deviation Rule, there is a 95% probability that students spent between:

Group of answer choices

$215 and $335

$235 and $315

$215 and $315

$255 and $295

$235 and $335

3) Based on national data, the amount of sleep per night of all U.S. adults follows a normal distribution with a mean of 7.5 hours and a standard deviation of 1.2 hours.

Using the Standard Deviation Rule, there is a 68% probability that U.S adults get between:

Group of answer choices

5.1 and 8.7 hours of sleep

3.9 and 11.1 hours of sleep

6.3 and 8.7 hours of sleep

6.3 and 9.9 hours of sleep

5.1 and 9.9 hours of sleep

4) According to national data, 70% of all credit card users in the U.S. do not pay their card bill in full every month (p = .70). Suppose that a random sample of size n = 500 credit cards users is chosen.

Use the Standard Deviation Rule and the properties of the sampling distribution of p-hat. There is a 95% chance that, in any random sample of 500 credit card users, the proportion of those who do not pay their bills in full every month will be between:

Group of answer choices

.60 and .80

.55 and .85

.64 and .76

.66 and .74

5) According to national data on the sleeping habits of adults, the amount of sleep per night of all U.S. adults follows a normal distribution with a mean of 7.5 hours and a standard deviation of 1.2 hours. A study surveyed a random sample of 700 U.S. adults and found that their average amount of sleep per night was 6.85 hours with a standard deviation of 1.88 hours.

Fill in the blank below with the appropriate number corresponding to the provided symbol.

6)

According to national data on the sleeping habits of adults, the amount of sleep per night of all U.S. adults follows a normal distribution with a mean of 7.5 hours and a standard deviation of 1.2 hours. A study surveyed a random sample of 700 U.S. adults and found that their average amount of sleep per night was 6.85 hours with a standard deviation of 1.88 hours.

Fill in the blank below with the appropriate number corresponding to the provided symbol.

=

About 24% of flights departing from New York's John F. Kennedy International Airport were delayed in 2009. Assuming that the chance of a flight being delayed has stayed constant at 24%, we are interested in finding the probability of 10 out of the next 100 departing flights being delayed. Noting that if one flight is delayed, the next flight is more likely to be delayed, which of the following statements is correct? .

(A) We can use the geometric distribution with n = 100, k = 10, and p = 0.24 to calculate this probability.

(B) We can use the binomial distribution with n = 10, k = 100, and p = 0.24 to calculate this probability.

(C) We cannot calculate this probability using the binomial distribution since whether or not one flight is delayed is not independent of another.

(D) We can use the binomial distribution with n = 100, k = 10, and p = 0.24 to calculate this probability

Some additional collected data is presented in the table below:

2. Identify if the distribution is binomial or not. If it is binomial, identify n and p.

(a) There are 5 people waiting to see the doctor. There is an equal chance that the doctor will see the next patient within seven minutes. What is the probability the doctor sees one of the waiting patients within the next minute?

(b) Based on past data, 85% of students attend graduation. Twenty-two students are randomly selected. What is the probability that at least 18 will attend graduation?

(c) Patients at two clinics are participating in a study. Clinic A has 35 patients. Clinic B has 30 patients. If 10 patients are chosen at random, what is the probability that 6 will be from Clinic A.

(d) The prevalence of malaria in Nigeria is 62%. What is the probability that you will need to select at least 6 people in order to find one that has malaria?

(e) The sensitivity of a pregnancy test is 98%. If 10 pregnant women are test, what is the probability that 8 or less will test positive for being pregnant?

The overhead reach distances of adult females are normally distributed with a mean of 197.5 cm and a standard deviation of 7.8 cm .

a. Find the probability that an individual distance is greater than 207.50 cm.
b. Find the probability that the mean for 15 randomly selected distances is greater than 196.20 cm.
c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

a. The probability is _________
(Round to four decimal places as needed.)

b. The probability is _________
(Round to four decimal places as needed.)

c. Choose the correct answer below.

A. The normal distribution can be used because the probability is less than 0.5

B. The normal distribution can be used because the finite population correction factor is small.

C. The normal distribution can be used because the mean is large.

D. The normal distribution can be used because the original population has a normal distribution.

Please show all steps:

A: Suppose that 90% of adults with allergies report symptomatic relief with a specific medication. If the medication is given to 10 new patients with allergies, what is the probability that it is effective in exactly six?

B: A small voting district has 110 female voters and 90 male voters. A random sample of 10 voters is drawn. What is the probability exactly 8 of the voters will be female?

C: A deck of cards contains 30 cards: 10 red cards and 20 black cards. 5 cards are drawn randomly without replacement. What is the probability that exactly 3 red cards are drawn?

D: The bivariate probability distribution of X and Y is given in the table below.

What is the conditional probability that X=3 given that Y=2?

Are X and Y independent? Explain