A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 39 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 39 weeks and that the population standard deviation is 3.5 weeks. Suppose you would like to select a random sample of 88 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is greater than 39.6. P(X > 39.6) =

(Enter your answers as numbers accurate to 4 decimal places.)

Find the probability that a sample of size n = 88 n=88 is randomly selected with a mean greater than 39.6. P(M > 39.6) =

(Enter your answers as numbers accurate to 4 decimal places.)

Let’s just say the standard deviation of those 8,000 students is 5.

1) What is the formula for standard deviation of a population the 8,000 students (please make sure the summation sign has a starting and ending number)? Can it ever be negative? In our example, what are the units of the standard deviation?

2) What does the Central Limit Theorem say about the standard deviation of the curve?

3) What is the standard deviation in our example? 5

4) What is the probability that a randomly picked sample has a point estimate within .5 of the actual mean ??

5) What is the probability that a randomly picked sample has a point estimate within 1 of the actual mean ??

6) Do you know whether our point estimate is higher or lower than the mean?

A certain large shipment comes with a guarantee that it contains no more than 20% defective items. If the proportion of items in the shipment is greater than 20%, the shipment may be returned. You draw a random sample of 10 items and test each one to determine whether it is defective.

1.             If in fact 20% of the items in the shipment are defective (so that the shipment is good, but just barely) what is the probability that 7 or more of the 10 sampled items are defective?
2.             Based on the answer to part (a), if 20% of the items in the shipment are defective would 7 defectives in a sample of size 10 be an unusually large number?
3.              If you found that 7 of the 10 sample items were defective, would this be convincing evidence that the shipment should be returned?
4.             If in fact 20% of the items in the shipment are defective, what is the probability that 2 or more of the 10 sampled items are defective?

Consider a finite population of size N in which the mean of the variable of interest Y is u. Suppose a sample of size n is taken from this population using simple random sampling with replacement. Suppose that the sample mean Y is used to estimate u.

(a) [3 marks] Calculate the probability of sample and probability of inclusion for this sam- pling protocol.

(b) (4 marks] Show that Y is unbiased for u.

(c) [4 marks] Calculate Var(Y). Make sure to provide complete details of your deriva- tion/calculation.

Hint: Define Z; to be the number of times that unit i apears in the sample, i = 1,2, ..., N. Find the distribution of Z; and use it parts (a) and (b). You may use Cov(Z;,Z;) = - Mz for i tj without proof.

The manager of a fast-food restaurant determines that the average time that her customers wait for service is 5.5 minutes. (a) Find the probability that a customer has to wait more than nine minutes. (Round your answer to three decimal places.)

(b) Find the probability that a customer is served within the first five minutes. (Round your answer to three decimal places.)

(c) The manager wants to advertise that anybody who isn't served within a certain number of minutes gets a free hamburger. But she doesn't want to give away free hamburgers to more than 2% of her customers. What should the advertisement say? (Give your answer to the nearest integer that satisfies the conditions.) "If you aren't served within ???? minutes, you get a free hamburger."

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 25 weeks. Assume that the length of unemployment is normally distributed with population mean of 25 weeks and the population standard deviation of 9 weeks. Suppose you would like to select a random sample of 35 unemployed individuals for a follow-up study. Round the answers of following questions to 4 decimal places.

1. What is the distribution of XX? XX ~ N(,)
2. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
3. What is the probability that one randomly selected individual found a job less than 27 weeks?
4. For 35 unemployed individuals, find the probability that the average time that they found the next job is less than 27 weeks.
5. For part d), is the assumption of normal necessary? NoYes

Advertisers contract with internet service providers and search engines to place ads on websites. They pay a fee based on the number of potential customers who click on their ad. Unfortunately, click fraud—the practice of someone clicking on an ad solely for the purpose of driving up advertising revenue—has become a problem. Business week reports that 40 percent of advertisers claim they have been a victim of click fraud. Suppose a simple random sample of 360 advertisers will be taken to learn more about how they are affected by this practice. (Round your answers to four decimal places.) (a) What is the probability that the sample proportion will be within ±0.04 of the population proportion experiencing click fraud? Incorrect: Your answer is incorrect. (b) What is the probability that the sample proportion will be greater than 0.45?

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 25 weeks. Assume that the length of unemployment is normally distributed with population mean of 25 weeks and the population standard deviation of 2 weeks. Suppose you would like to select a random sample of 39 unemployed individuals for a follow-up study. Round the answers of following questions to 4 decimal places.

1. What is the distribution of XX? XX ~ N(,)
2. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
3. What is the probability that one randomly selected individual found a job more than 25 weeks?
4. For 39 unemployed individuals, find the probability that the average time that they found the next job is more than 25 weeks.
5. For part d), is the assumption of normal necessary? No Yes

A recent survey reported that 50​% of​ 18- to​ 29-year-olds in a certain country own tablets. Using the binomial​ distribution complete.

c. What is the probability that in the next six​ 18- to​ 29-year-olds surveyed, at least four will own a​ tablet?

The probability is_______________.

d.The standard deviation of the number of? 18- to? 29-year-olds who own tablets out of six surveyed ?(Type an integer or a decimal. Round to four decimal places as? needed.)

e. What assumptions do you need to make in? (a) through? (c)? Select all that apply. A. Each observation is classified into one of two mutually exclusive and collectively exhaustive categories. B. The outcome of any observation is independent of the outcome of any other observation.

if you tell me how to do on my TI-84 that is great too.

1. An imaginary study states that an American household spends an average of $1250 per year on soft drinks. The standard deviation for the study is $225. If 30 American households are selected at random, what is the probability that they spend an average of between $1180 and $1270 per year on soft drinks?

2. The average number of deaths per week for Covid 19 patients in the U.S. since March 21st is 9,433, with a standard deviation of 4733. If a week is chosen at random, what is the probability that there were more than 6000 deaths in that week?

3. The average distance a baseball was tossed by students trying out for the little league team was 65 ft., with a standard deviation of 8 ft. If the top 20% of these players will be chosen for the team, what is the least distance necessary to throw the ball to make the team?