cA Christmas tree provider sells trees on Dec. 20th. They sell trees for 5 full days, closing the lot at the end of the day on December 24th. Based on past sales data, they decided to cut down 220 trees for this year's selling season. Each cut tree has a 70% chance of being a healthy tree that a customer would purchase and a 30% chance of being an unhealthy tree that nobody wants to purchase. On each of the 5 selling days, the number of customers who show up prepared to purchase a tree is normally distributed with an average of 30 and a standard deviation of 5.

a) On average, How many healthy trees do they have?

b) What is the likelihood they end up with 168 or more healthy trees?

c) What is the likelihood that 168 customers or more visit to purchase a tree?

d) What is the likelihood that more customers visit over the 5 days than they can provide healthy trees for? (stockout)

e) How many trees do they need to cut down to ensure stocking out is less than or equal to 10%?

f) Suppose it costs $25 for each tree they cut down and healthy trees are sold for $100. Is it better to stick with the 220 tree strategy or change it to what you found in part e?

7. A number of minor automobile accidents occur at various high-risk intersections in Teton County despite traffic lights. The Traffic Department claims that a modification in the type of light will reduce these accidents. The county commissioners have agreed to a proposed experiment. Eight intersections were chosen at random, and the lights at those intersections were modified. At the .01 significance level, is it reasonable to conclude that the modification reduced the number of traffic accidents?

What do these four forecasting techniques mean and when should I use them?

1) Moving Average Technique

2) Simple Linear Regression Technique

3) Multiple Linear Regression Analysis Technique

4) Exponential Smoothing Forecasting Technique

Suppose that a random sample of nine recently sold houses in a certain city has a mean sales price of

$280,000

, with a standard deviation of

$12,000

. Under the assumption that house prices are normally distributed, find a

90%

confidence interval for the mean sales price of all houses in this community. Then complete the table below.

Carry your intermediate computations to at least three decimal places. Round your answers to the nearest whole number. (If necessary, consult a list of formulas.)

A normal population has a mean of 65 and a standard deviation of 13. You select a random sample of 16. Compute the probability that the sample mean is:

Thirty-two small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5 reported cases of larceny per year. Assume that σ is known to be 42.5 cases per year.

(a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(b) Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(c) Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(d) Compare the margins of error for parts (a) through (c). As the confidence levels increase, do the margins of error increase?

As the confidence level increases, the margin of error increases.As the confidence level increases, the margin of error decreases.    As the confidence level increases, the margin of error remains the same.

(e) Compare the lengths of the confidence intervals for parts (a) through (c). As the confidence levels increase, do the confidence intervals increase in length?

As the confidence level increases, the confidence interval decreases in length.As the confidence level increases, the confidence interval remains the same length.    As the confidence level increases, the confidence interval increases in length.

Question 3 A study of workers earning minimum wage were grouped into various categories, which can be interpreted as events when a worker is selected at random. Considering the following events: E: worker is under 20 years of age F: worker is white G: worker is female Describe the following events in words • E’ • F ꓵ G’ • E ꓴ G Question 4 if a single card is drawn from an ordinary deck of cards, find the probability it will be a red or a face card. (Face cards are Jack, Queen, and King) Question 5 Supposed two fair die are rolled. Find the probability the first die shows a two or the sum of the result is six or seven. Question 6 If two fair die are rolled find the probability that the sum of the numbers rolled is greater than three. (Be careful of the phrase greater than). please show work or give explnation so i can try and figure out how to do the problems

Find a value of the standard normal random variable z ​, call it

z 0z0​,

such that the following probabilities are satisfied.

a.

z 0z0equals=nothing

​(Round to two decimal places as​ needed.)b.

z 0z0equals=nothing

​(Round to two decimal places as​ needed.)c.

z 0z0equals=nothing

​(Round to two decimal places as​ needed.)d.

z 0z0equals=nothing

​(Round to two decimal places as​ needed.)e.

z 0z0equals=nothing

​(Round to two decimal places as​ needed.)f.

z 0z0equals=nothing

​(Round to two decimal places as​ needed.)g.

z 0z0equals=nothing

​(Round to two decimal places as​ needed.)h.

z 0z0equals=nothing

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

Unit 003 Review of Material that has been covered

There are two parts to each question . Part 1 just give the null hypothesis, alternative hypothesis and test statistic formula. for part 1 don't work it out just write the formula.

Part 2-This is where you work all five steps. Show all work.

#5

A randomly selected list of holiday food items was generated. Thirty King Kong stores were surveyed as to what the cost of the list of items would cost. The mean and standard deviation is recorded in the table below. Fifty Saves Alot stores were surveyed in a similar manner and the mean and the standard deviation was recorded below. Test whether the King Kong mean amount spent is less than the Saves Alot amount spent. a = 0.01.

Customers arrive at a local grocery store at an average rate of 2 per minute.

(a) What is the chance that no customer will arrive at the store during a given two minute period?

(b) Since it is a “Double Coupon” day at the store, approximately 70% of the customers coming to the store carry coupons. What is the probability that during a given two-minute period there are exactly four (4) customers with coupons and one (1) without coupons?

(c) Divide one given hour into 30 two-minute periods. Suppose that the numbers of customers arriving at the store during those periods are independent of each other. Denote by X the number of the periods during which exactly 5 customers arrive at the store and 4 of them carry coupons. What is the probability that X is at least 2?

(d) What is the probability that exact 4 customers coming to the store during a given two-minute period carry coupons?

An exam is given to select the top 15% of incoming students for a special honors program. The cutscore for the exam is 28 points. The mean of the test scores is 24 points. What is the standard deviation of the test scores?

In a USA Today article about an experimental vaccine for children the data found in the table below was presented. Using the technique of Chi Square use a .05 significance level to test if there is an association between treatment type and outcome of flu. Does the vaccine appear to be effective? (Is there an association?)

Developed flu?

yes no

vaccine 14 656

placebo 95 137

Do out-of-state motorists violate the speed limit more frequently than in-state motorists? This vital question was addressed by the highway patrol in a large eastern state. A random sample of the speeds of 2,500 selected cars was categorized according to whether the car was registered in the state or in some other state and whether or not the car was violating the speed limit. The data follow.

In state speeding cars: 521

Out of state speeding cars: 328

In state not speeding cars: 1141

Out of state not speeding cars: 510

a.) Do these data provide enough evidence to support the highway patrol's claim at the 5% significance level? Your conclusion must be in terms of the P-Value. Show all necessary work.

b). What type of error is possible and describe this error in terms of the problem?

c). Estimate the difference in the actual percentage of In State and Out of State speed limit violators using a 95% confidence interval. Show all necessary work. Using this interval estimation, is there sufficient evidence to support the highway patrol's claim? Explain Carefully.

d). Carefully interpret the confidence interval estimation.

Use non-parametrics/Mann-Whitney test if the problem calls for it- Does it?

find the multiplicative inverse of 32(mod 101). answer must range from 0 to 100