Time spent using​ e-mail per session is normally​ distributed, with mu equals 7 minutes and sigma equals 2 minutes. Assume that the time spent per session is normally distributed. Complete parts​ (a) through​ (d). a. If you select a random sample of 25 ​sessions, what is the probability that the sample mean is between 6.8 and 7.2 ​minutes?

Acme Outdoors Co. is introducing a new line of sport all-terrain vehicles (ATVs). Acme is considering program proposals from two competing companies: A & B. A's marketing plan is expected to generate high sales with a 75% probability and only a 25% likelihood of low sales.

An alternative marketing plan from company B could result in an initial 60% likelihood of high ATV sales and 40% probability of low sales. But company B's offer also contains a provision for an optional follow-on promotion if a low response is returned. If an optional follow-on ATV promotion is conducted by company B, there is a 70% chance of ultimately realizing high sales.

Draw an decision tree diagram with branches labeled and probabilities, do not solve.

“Larry’s logs” is planning to change the supplier. For complete analysis he needs to compute the Multifactor Productivity (MFP) for each supplier. He expects to produce 240 units using old supplier, and 260 using the new supplier. He pays $10 per hour, and will use 300 labor hours with current supplier and 308 hours with the new supplier. Other costs will be consistent across both suppliers (materials are $10 per log), using a total of 100 logs; capital costs will be $350 and energy $150).

What is the total cost for current and new supplier?

What is the multifactor productivity for the current and new supplier?

What is percent change in multifactor productivity?

1)    A lawn and garden retailer operates 4 stores in the DFW Metroplex. One of its most popular items is a lawn tractor. Weekly customer demand is distributed N(10,5²) at each store. Each store replenishes its stock to 15 lawn tractors at the start of each week. Note: Assume that weekly demands at each store are independent.

a)   Consider just one store. What is the probability of a stockout in that store?

b)   What is the probability of a stockout in at least two of the four stores?

c)   Suppose that the four stores decide to pool their stock. Specifically, they decide to pool their weekly allocations (4 X 15 = 60) in a centrally located warehouse and draw from it as needed to satisfy their demand. How often will a store experience a stockout now?

a) What is an exponential distribution (include an APA citation)? ___________________________

b) When would you use an exponential distribution? ________________________

c) What is a binomial distribution (include an APA citation)?_______________________

d) When would you use a binomial distribution? ___________________

3. Task

Run these commands in R, then use your own words to describe what the resulting numbers represent.  You can get some information about the functions by using the help commands in R (such as ?pbinom to get information about the pbinom() command in R):

a) pbinom(q=5, size=10, prob=1/6)

b)

n=10
p=.5
x=9
pbinom(x, n, p)

c) punif(5, min=1, max=10) - punif(4, min=1, max=10)

1.

a. A researcher wishes to estimate the proportion of adults who have​ high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.3 with 99% confidence?

b.

it is believed that people prefer rubies over other gems. In a recent simple random survey of 150 people, 63 said they would prefer a ruby over other gems. Use this sample data to complete a hypothesis test to determine if a majority of people would prefer a ruby. over other gems at the 0.01 significance level.

Be sure to include all the steps for a complete hypothesis test - start and end in context, test conditions, show formulas and numbers used, clearly state REJECT or FAIL TO reject.

c.

If 12 jurors are randomly selected from a population that is 45% Hispanic, what is the probability that 2 or fewer jurors will be Hispanic?

Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a certain article, the mean of the x distribution is about $49 and the estimated standard deviation is about $8.

(a) Consider a random sample of n = 60 customers, each of whom has 10 minutes of unplanned shopping time in a supermarket. From the central limit theorem, what can you say about the probability distribution of x, the average amount spent by these customers due to impulse buying? What are the mean and standard deviation of the x distribution?

The sampling distribution of x is not normal.
The sampling distribution of x is approximately normal with mean μ_x = 49 and standard error σ_x = $8.    
The sampling distribution of x is approximately normal with mean μ_x = 49 and standard error σ_x = $0.13.
The sampling distribution of x is approximately normal with mean μ_x = 49 and standard error σ_x = $1.03.

Is it necessary to make any assumption about the x distribution? Explain your answer.

It is not necessary to make any assumption about the x distribution because μ is large.
It is necessary to assume that x has an approximately normal distribution.    
It is not necessary to make any assumption about the x distribution because n is large.
It is necessary to assume that x has a large distribution.

(b) What is the probability that x is between $47 and $51? (Round your answer to four decimal places.)


(c) Let us assume that x has a distribution that is approximately normal. What is the probability that x is between $47 and $51? (Round your answer to four decimal places.)


(d) In part (b), we used x, the average amount spent, computed for 60 customers. In part (c), we used x, the amount spent by only one customer. The answers to parts (b) and (c) are very different. Why would this happen?

The sample size is smaller for the x distribution than it is for the x distribution.
The standard deviation is smaller for the x distribution than it is for the x distribution.    
The x distribution is approximately normal while the x distribution is not normal.
The mean is larger for the x distribution than it is for the x distribution.
The standard deviation is larger for the x distribution than it is for the x distribution.

In this example, x is a much more predictable or reliable statistic than x. Consider that almost all marketing strategies and sales pitches are designed for the average customer and not the individual customer. How does the central limit theorem tell us that the average customer is much more predictable than the individual customer?

The central limit theorem tells us that small sample sizes have small standard deviations on average. Thus, the average customer is more predictable than the individual customer.
The central limit theorem tells us that the standard deviation of the sample mean is much smaller than the population standard deviation. Thus, the average customer is more predictable than the individual customer.    

The weights for newborn babies is approximately normally distributed with a mean of 5lbs and a standard deviation of 1.5lbs. Consider a group of 1,000 newborn babies:

How many would you expect to weigh between 4-7lbs?

How many would you expect to weigh less than 6lbs?

How many would you expect to weigh more than 5lbs?

How many would you expect to weigh between 5-10lbs?

In 2018 and 2019, Health Canada commissioned two national surveys on the use of cannabis among people aged 20 to 24. They found 175 users out of the 1000 surveyed individuals in 2018 and 230 out of the 1100 sample in 2019.

1. (a) Test the hypothesis that there has been a change in the proportion of cannabis users in the 20-24 age

   group population between 2018 and 2019. Use the critical value approach and a 0.05 level of

   significance.

2. (b) Find the p-value for your result in (a) above.

3. (c) Calculate a 95% two-sided confidence interval for the true difference using the data provided.

4. (d) Explain how the p-value and the confidence interval are or are not consistent with your result in

   part (a) above.

Use the accompanying paired data consisting of registered boats​ (tens of​ thousands) and manatee fatalities from boat encounters. Let x represent the number of registered boats and let y represent the corresponding number of manatee deaths. Use the given number of registered boats and the given confidence level to construct a prediction interval estimate of manatee deaths. Use x=89 (for 89​0,000 registered​ boats) with a 99​% confidence level.

Boats (tens of thousands)   Manatees
67    54
68    37
66    34
73    49
74    40
70    59
76    56
82    67
83    84
83    80
90    82
91    94
95   74
93   69
97   78
99   93
97   73
98   91
98   97
91   81
90   87
90   82
89   73
90   7

Find the indicated prediction interval.

___manatees < y < manatees

​(Round to three decimal places as​ needed.)

A dairy scientist is testing a new feed additive. She chooses 13 cows at random from a large population. She randomly assigns n_old = 8 to the old diet and n_new = 5 to a new diet including the additive. The cows are housed in 13 widely separated pens. After two weeks, she milks each cow and records the milk produced in pounds:

Old Diet: 43, 51, 44, 47, 38, 46, 40, 35 New Diet: 47, 75, 85, 100, 58

Let μnew and μold be the population mean milk productions for the new and old diets, respectively. She wishes to test H0 : μnew − μold = 0 against HA : μnew − μold ̸= 0 using α = 0.05.

(a) Graph the data as you see fit. Why did you choose the graph(s) that you did and what does it (do they) tell you?

(b) Choose a test appropriate for the hypotheses and justify your choice based on your answer to part (a). Then perform the test by computing a p-value, and making a reject or not reject decision. Do this without R and show your work. (Also do it with R, if you wish, to check your work). Finally, state your conclusion in the context of the problem.

n a 2008​ survey, people were asked their opinions on astrology​ - whether it was very​ scientific, somewhat​ scientific, or not at all scientific. Of 1438 who​ responded, 76 said astrology was very scientific. a. Find the proportion of people in the survey who believe astrology is very scientific. b. Find a​ 95% confidence interval for the population proportion with this belief. c. Suppose a TV news anchor said that​ 5% of people in the general population think astrology is very scientific. Would you say that is​ plausible? Explain your answer. a. The proportion of people in the survey who believe astrology is very scientific is . 0529. ​(Round to four decimal places as​ needed.) b. Construct the​ 95% confidence interval for the population proportion with the belief that astrology is very scientific. left parenthesis nothing comma nothing right parenthesis ​(Round to three decimal places as​ needed.) Enter your answer in the edit fields and then click Check Answer.

Consider two random variables X and Y, with Y = (a+bX)

- Find E(Y)

- Find Cov(X,Y)

- Find Corr(X,Y)