1 supposenbsp x n that is x has a normal distribution with

Assignment Help Microeconomics

Reference no: EM13375099

1. Suppose X ~ N. That is, X has a normal distribution with μ=30 and σ²=144.

1a. Find a transformation of X that will give it a mean of zero and a variance of one(ie., standardize X).

1b. Find the probability that 18< x<36.

1c. Supposing Y = 10 + 5X, find the mean of Y.

1d. Find the variance of Y.

2. A bank has been receiving complaints from real estate agents that their customers have been waiting too long for mortgage confirmations. The bank prides itself on its mortgage application process and decides to investigate the claims. The bank manager takes a random sample of 20 customers whose mortgage applications have been processed in the last 6 months and finds the following wait times (in days):

5, 7, 22, 4, 12, 9, 9, 14, 3, 6, 5, 8, 10, 17, 12, 10,9, 4, 3, 13

Assume that the random variable measures the number of days a customer waits for mortgage processing at this bank, and assume that is normally distributed.

2a. Find the sample mean of this data X' .

2b. Find the sample variance of . Find the variance of X'.

For (c), (d), and (e), use the appropriate t-distribution

2c. Find the 90% confidence interval for the population mean (μ).

2d. Test the hypothesis that μis equal to 7 at the 95% confidence level. (Should you do a one-tailed or two-tailed test here?)

2e. What is the approximate p-value of this hypothesis?

3. My nephew was born last summer. He has 19 cousins on his father's side (it's a big family). I wish to know the mean, μ_x, of the distribution of the ages of my nephew's cousins (which is the variable X). I take a sample of 4, with ages X₁, X₂, X₃ and X₄. These are all drawn from the same underlying population. Instead of calculating the sample mean of these four, I do the following calculation to create an estimator of , which I call X.

722_Find a transformation of X.png

3a. Explain what it means to say that is unbiased?

3b. Show that X* is unbiased.

3c. If the variance of is 15, what is the variance of X*?

3d. If the variance of is 15, what is the variance of the X'?

3e. Which estimator is more efficient, the sample mean or X*? Explain.

Reference no: EM13375099

Questions Cloud

Discuss in detail the role of both informational and : discuss in detail the role of both informational and normative influence in nazi germany and the

1 refer to the following table and assume that the total : 1. refer to the following table and assume that the total labor supply in taiwan is 4 and the total labor supply in

The focus of your paper must be a subculture of people that : the focus of your paper must be a subculture of people that exists within your local community. the subculture you

Q : question 1suppose x n30 144 and wn40225.a. if x and w are

1 supposenbsp x n that is x has a normal distribution with : 1. supposenbsp x n. that is x has a normal distribution with mu30 and sigma2144.1a. find a transformation of x that

How do we respond to emotionwhat causes emotion what are : how do we respond to emotion?what causes emotion ?what are mood and how they differ from emotion ?how can a facial

Describe the four levels of language structure : describe the four levels of language structure and

Explain how both normative and informational social : explain how both normative and informational social influence worked to convince stanley milgrams 1974 participants to

Compare and contrast how cognitive dissonance theory and : compare and contrast how cognitive dissonance theory and self-perception theory would explain the festinger and

User Account

All Pages