In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. Do you try to pad an insurance claim to cover your deductible? About 39% of all U.S. adults will try to pad their insurance claims! Suppose that you are the director of an insurance adjustment office. Your office has just received 126 insurance claims to be processed in the next few days. Find the following probabilities. (Round your answers to four decimal places.)

(a) half or more of the claims have been padded

(b) fewer than 45 of the claims have been padded

(c) from 40 to 64 of the claims have been padded

(d) more than 80 of the claims have not been padded

Suppose that the average number of Facebook friends users have is normally distributed with a mean of 121 and a standard deviation of about 40. Assume forty-five individuals are randomly chosen. Answer the following questions. Round all answers to 4 decimal places where possible.

What is the distribution of x? x ~ N(___,____)

For the group of 45, find the probability that the average number of friends is less than 115. _____

Find the first quartile for the average number of Facebook friends. ____

For part b), is the assumption that the distribution is normal necessary? Yes or No

Suppose that Westside Auto, a manufacturer of automobile generators with D = 13,000 units per year, C_h = (2.00) (0.20) = $0.40, and C_o = $25, decided to operate with a backorder inventory policy. Backorder costs are estimated to be $5 per unit per year. Identify the following. (Assume 250 working days per year. Round your answers to two decimal places.)

(a)

Minimum cost order quantity

(b)

Maximum number of backorders

(c)

Maximum inventory

(d)

Cycle time (in days)

days

(e)

Total annual cost (in $)

$

We learned this week that a chi-square analysis has requirements for variables that are unique from the other analyses we've considered. For instance, the variables must be exhaustive, so they must include all possible answers. For this reason, something like yes and no are valid since those would be the only two options, unless you had someone who couldn't answer it for various reasons. Similarly, it needs to be mutually exclusive, so someone couldn't be in two categories at the same time. This should make sense as you want to see if there's a relationship between the variables and you need to compare the expected counts with the actual counts. This is a very unique kind of test as you're only able to see categories - you wouldn't be able to tell if someone was at the high or low end of a category, for instance. Therefore, while it provides a quick and easy way to see if there are general differences, you don't necessarily know how extreme the situations are. Do you feel it's more important to have the quick and easy categorical results, or have the more detailed numerical results, and why?

The A&M Hobby Shop carries a line of radio-controlled model racing cars. Demand for the cars is assumed to be constant at a rate of 50 cars per month. The cars cost $80 each, and ordering costs are approximately $15 per order, regardless of the order size. The annual holding cost rate is 20%.

(a)

Determine the economic order quantity and total annual cost (in $) under the assumption that no backorders are permitted. (Round your answers to two decimal places.)

Q* = TC= $

(b)

Using a $45 per-unit per-year backorder cost, determine the minimum cost inventory policy and total annual cost (in $) for the model racing cars. (Round your answers to two decimal places.)

Q* = TC= $

(c)

What is the maximum number of days a customer would have to wait for a backorder under the policy in part (b)? Assume that the Hobby Shop is open for business 300 days per year. (Round your answer to two decimal places.)

days

(d)

Would you recommend a no-backorder or a backorder inventory policy for this product? Explain.

Yes, the maximum wait is less than a week and the backorder case has a lower cost than the EOQ case.Yes, the maximum wait is over a week long, but the cost savings of the backorder case is large enough to justify a long wait.     No, the maximum wait is over a week long and the EOQ case has a lower cost than the backorder case.No, the maximum wait is over a week long, which does not justify the cost savings of the backorder case.No, the maximum wait is less than a week but the EOQ case has a lower cost than the backorder case.

(e)

If the lead time is six days, what is the reorder point for both the no-backorder and backorder inventory policies? (Round your answers to two decimal places.)

EOQ r= Backorder r=

A farmer's marketing cooperative recorded the volume of wheat harvested by its members from 1991-2004. The cooperative is interested in detecting the long-term trend of the amount of wheat harvested. The data collected is shown in the table.

                                     Wheat Harvested by Coop. Member

            Year      Time          (y, in thousands of bushels)    

            1991         1                               75

            1992         2                               78

            1993         3                               82

            1994         4                               82

            1995         5                               84

            1996         6                               85

            1997         7                               87

            1998         8                               91

            1999         9                               92

            2000        10                              92

            2001        11                              93

            2002        12                              96

            2003        13                            101

            2004        14                            102                       

Find the least squares prediction equation for the model. Use excel to conduct data analysis. Provide detailed interpretation of the results.

A certain health maintenance organization (HMO) wishes to study why patients leave the HMO. A SRS of 396 patients was taken. Data was collected on whether a patient had filed a complaint and, if so, whether the complaint was medical or nonmedical in nature. After a year, a tally from these patients was collected to count number who left the HMO voluntarily. Here are the data on the total number in each group and the number who voluntarily left the HMO:

If the null hypothesis is H0:p1=p2=p3 and using α=0.05 then do the following: (Use two decimal places when appropriate)

(a) Find the expected number of people with no complaint who leave the HMO:

(b) Find the expected number of people with a medical complaint who leave the HMO:

(c) Find the expected number of people with a nonmedical complaint who leave the HMO:

(d) Find the test statistic:

(e) Find the degrees of freedom:

(f) Find the critical value:

(g) The final conclusion is

A. We can reject the null hypothesis that the proportions are equal.
B. There is not sufficient evidence to reject the null hypothesis.

The Food Marketing Institute shows that 18% of households spend more than $100 per week on groceries. Assume the population proportion is p = 0.18 and a sample of 700 households will be selected from the population. Use z-table.

Calculate (), the standard error of the proportion of households spending more than $100 per week on groceries (to 4 decimals).

What is the probability that the sample proportion will be within +/- 0.02 of the population proportion (to 4 decimals)?

What is the probability that the sample proportion will be within +/- 0.02 of the population proportion for a sample of 1,600 households (to 4 decimals)?

Suppose a random sample of size 60 is selected from a population with = 8. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate). The population size is infinite (to 2 decimals). The population size is N = 50,000 (to 2 decimals). The population size is N = 5,000 (to 2 decimals). The population size is N = 500 (to 2 decimals).

Bob is a recent law school graduate who intends to take the state bar exam. According to the National Conference on Bar Examiners, about 55% of all people who take the state bar exam pass. Let n = 1, 2, 3, ... represent the number of times a person takes the bar exam until the first pass.

(a) Write out a formula for the probability distribution of the random variable n. (Use p and n in your answer.)
P(n) =

(b) What is the probability that Bob first passes the bar exam on the second try (n = 2)? (Use 3 decimal places.)


(c) What is the probability that Bob needs three attempts to pass the bar exam? (Use 3 decimal places.)


(d) What is the probability that Bob needs more than three attempts to pass the bar exam? (Use 3 decimal places.)


(e) What is the expected number of attempts at the state bar exam Bob must make for his (first) pass? Hint: Use μ for the geometric distribution and round.

3. Jim is a 60-year-old male in reasonably good health. He wants to take out a $75,000 term (that is, straight death benefit) life insurance policy until he is 65. The policy will expire on his 65th birthday. The probability of death in a given year is provided by the Vital Statistics Section of the Statistical Abstract of the United States (116^th edition)

Jim is applying to Big Rock Insurance Company for his term insurance policy.

1. What is the probability that Jim will die in his 60th year? Using this probability and the $75,000 death benefit, what is the expected cost to Big Rock Insurance?

2. Repeat part (a) for years 61, 62, 63, and 64. What would be the total expected cost to Big Rock Insurance over the years 60 through 64?

3. If Big Rock Insurance wants to make a profit of $850 above the expected total cost paid out for Jim’s death, how much should it charge for the policy?

4. If Big Rock Insurance Company charges $6500 for the policy, how much profit does the company expect to make?

5. Let X1,...,Xn ∼ Geo(θ).

   1. (a) Find a 90% asymptotic confidence interval for θ.

   2. (b) Find a 99% asymptotic lower confidence intervals for φ = 1/θ, the expected number of trials until the first success.

A random sample of 81 cars traveling on a section of an interstate showed an average speed of 68 mph. The distribution of speeds of all cars on this section of highway is normally distributed with a standard deviation of 10.5 mph.

The 94.52 confidence interval for μ is from _____ to ____?

The company Hanna Properties specializes in custom-home resales in the Equestrian Estates, an exclusive subdivision in Phoenix, Arizona. Thirty-three properties were randomly selected and square footage, number of bedrooms, number of bathrooms, number of days on the market, and selling price (in thousands of dollars) were investigated. In this problem, you will perform a regression analysis for selling price in terms of the other four variables

The data is available as Properties.txt

SALe_PRICE   SQFT   BEDROOMS   BATHS   DAYS
715   5232   5   5   8
583   4316   4   5   140
484   4238   4   4   229
425   3600   4   4   386
418   4000   4   3   0
418   3730   5   4   260
407   3005   4   3   81
405   3800   4   3   52
385   4127   4   4   108
336   3800   4   3   108
330   3200   4   3   52
330   3319   4   3   66
330   3259   4   3   121
319   3200   4   3   103
314   3400   5   3   60
308   3000   4   3   266
308   3007   4   3   144
297   3041   4   3   74
292   3043   4   3   110
286   3406   4   3   10
285   2539   4   2   44
283   3013   4   3   58
282   3022   4   3   171
272   2792   4   3   274
270   3407   4   3   31
267   3275   4   3   361
266   2826   4   3   88
266   2820   4   3   88
266   2826   4   3   252
264   2610   4   3   48
258   2790   3   3   33
253   2400   4   2   57
249   2780   3   3   223

Need questions (g) through (i) to be done with the R program please, I really need help with the R coding aspect.

(g) Do the data provide sufficient evidence to conclude that, taken together, square footage, number of bedrooms, number of bathrooms, and number of days on the market are useful for predicting selling price? Perform the required hypothesis test at the 1% significance level.

(h) For all homes in the Equestrian Estates that have 3200 sq ft, 4 bedrooms, 3 bathrooms, and that remain on the market for 60 days,
(i) Obtain a point estimate for the mean selling price.
(ii) Obtain a 95% confidence interval for the mean selling price.
(iii) Determine the predicted selling price.
(iv) Determine a 95% prediction interval for the selling price.

(i) Apply backward elimination to get a new model involving fewer predictors? What features make the new model better than the old one?

Explain how a hypothesis testing for a mean is similar to a hypothesis test for a proportion. Then explain how z-test for a mean is different than a t-test for a mean.