Assume that X is normally distributed with a mean of 15 and a standard deviation of 2. Determine the value for x that solves:

P(X>x) = 0.5.

P(X < 13).

P(13 < X < 17).

Anystate Auto Insurance Company took a random sample of 358 insurance claims paid out during a 1-year period. The average claim paid was $1530. Assume σ = $230.

Find a 0.90 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

Find a 0.99 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

1. Given the data below, calculate the mean, calculate the standard deviation and explain the significance of each in the context of the data.

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 $39 and the estimated standard deviation is about $7.

(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 approximately normal with mean μ_x = 39 and standard error σ_x = $0.90.The sampling distribution of x is approximately normal with mean μ_x = 39 and standard error σ_x = $7.    The sampling distribution of x is approximately normal with mean μ_x = 39 and standard error σ_x = $0.12.The sampling distribution of x is not normal.

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

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

(b) What is the probability that x is between $37 and $41? (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 $37 and $41? (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 standard deviation is larger for the x distribution than it is for the x distribution.The mean is larger 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 standard deviation is smaller for the x distribution than it is for the x distribution.The sample size is smaller 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.

1. Explain why the probability of a number X is thought of as different under discrete versus continuous distributions.

Thirty-one 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 45.1 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.) lower limit upper limit margin of error (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.) lower limit upper limit margin of error (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.) lower limit upper limit margin of error

1. The Fairfax County Economic Development Authority is concerned that increasing traffic congestion in the county is deterring new business from moving to the area. A sample of 49 commuters in Fairfax County were asked how long it took them to get to work in the morning. A sample mean of 26 minutes and sample standard deviation of 8 minutes was obtained.
   1. Construct a 96% confidence interval for the mean commute time to work in Fairfax County.
   2. Across the Potomac, Montgomery County is competing with Fairfax to attract business. A sample of 36 Montgomery County commuters were asked how long it took to get to work in the morning. A sample mean of 23 minutes and a sample standard deviation of 10 minutes was obtained. Construct a 96% confidence interval for the mean commute time to work in Montgomery County.
   3. Based on your calculations in (a) and (b), is there a difference on the average commute time in the two competing counties? Justify briefly using the numbers in your calculations.

X ∼ NBD(r, p). Derive the var(X).

Discuss what are some of the possible "lurking variables" that may exist from the below scenario.

A correlation was found between high blood pressure and cancer rates. (People with high blood pressure were more likely to develop cancer than people with low blood pressure.) It was concluded that high blood pressure causes cancer.

QUESTION 6. Z is a standard normal variable. Find the value of Z in the following. (12 points)

2 Points each

a. The area to the left of Z is 0.8554

b. The area to the right of Z is 0.1112.

c. The area to the left of -Z is 0.0681.

d. The area to the right of -Z is 0.9803.

e. The area between 0 and Z is 0.4678.

f. The area between -Z and Z is 0.754.

1. In a typical month, an insurance agent presents life insurance plans to 40 potential customers. Historically, one in four such customers chooses to buy life insurance from this agent. You may treat this as a binomial experiment.
   1. What is the probability of success for this problem?
   2. What is the total number of trials in this problem?
   3. Create a probability distribution table which includes the value for the random variable and the probability of each possible outcome of the random variable. Also create the cumulative probability column.
   4. What is the probability that exactly five customers will buy life insurance from this agent in the coming month?
   5. What is the probability that no more than 10 customers will buy life insurance from this agent in the coming month?
   6. What is the probability that at least 20 customers will buy life insurance from this agent in the coming month?
   7. Determine the mean and standard deviation of the number of customers who will buy life insurance from this agent in the coming month?
   8. What is the probability that the number of customers who buy life insurance from this agent in the coming month will lie within two standard deviations of the mean?

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A professor in a graduate course wants to form a team of three students to represent the class at a national case competition? Of the 20 students in the class, 5 have undergraduate degrees in Economics, 9 in Engineering and 6 in business. If the team is formed at random, what is the probability that there will be at least two students with different undergraduate majors on the team?

Which of the following is not a drawback to a longitudinal study?