Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 78 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean μ = 78 tons and standard deviation σ = 1.2 ton.

(a) What is the probability that one car chosen at random will have less than 77.5 tons of coal? (Round your answer to four decimal places.)


(b) What is the probability that 21 cars chosen at random will have a mean load weight x of less than 77.5 tons of coal? (Round your answer to four decimal places.)


(c) Suppose the weight of coal in one car was less than 77.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment?

Yes No    

Suppose the weight of coal in 21 cars selected at random had an average x of less than 77.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Why?

Yes, the probability that this deviation is random is very small. Yes, the probability that this deviation is random is very large.     No, the probability that this deviation is random is very small. No, the probability that this deviation is random is very large.

A manager of an inventory system believes that inventory models are important decision-making aids. The manager has experience with the EOQ policy, but has never considered a backorder model because of the assumption that backorders were “bad” and should be avoided. However, with upper management's continued pressure for cost reduction, you have been asked to analyze the economics of a backorder policy for some products that can possibly be backordered. For a specific product with D = 800 units per year, Co = $150, Ch = $5, and Cb = $30, what is the difference in total annual cost between the EOQ model and the planned shortage or backorder model? If the manager adds constraints that no more than 25% of the units can be backordered and that no customer will have to wait more than 15 days for an order, should the backorder inventory policy be adopted? Assume 250 working days per year.

Supposed to waiting to my pro price is not only distributed with a mean of 18 minutes and serve Eva tion 4 minutes and I giving mom for 31 days determine the probability that the average waiting time is less than 6 minutes

We will check to see if the mean salaries for Nursing School graduates for their respective schools are different. A sample of 36 graduates from School #1 found a mean hourly wage of $28.00 an hour. The school stated that the standard deviation for salaries for their graduates was $6.00 an hour. A sample of 40 graduates from School #2 found a mean hourly wage of $26.00 an hour. The standard deviation for the graduates of this school was known to be $5.00 an hour. At an alpha of .05 do we have evidence to refute the claim that there is no difference in these average salaries?

a. Null/Alternate Hypotheses

b. Test Statistic

c. Critical regions

d. Reject/Fail to Reject

e. Find the p-value

f. Answer the question.

A manufacturer fills soda bottles. Periodically they test to see if there is a difference in the amount of soda put in cola and diet cola bottles. A random sample of 14 cola bottles contains an average of 502 mL of cola with a standard deviation of 4 mL. A random sample of 16 diet cola bottles contains an average of 499 mL of cola with a standard deviation of 5 mL. Test the claim that there is a difference in the fill levels of the two types of soda using a 0.01 level of significance. Assume that the population variances are different since different machines are used for the filling process.

From public records, individuals were identified as having been charged with drunken driving not less than 6 months or more than 12 months from the starting date of the study. Two random samples from this group were studied. In the first sample of 29 individuals, the respondents were asked in a face-to-face interview if they had been charged with drunken driving in the last 12 months. Of these 29 people interviewed face to face, 12 answered the question accurately. The second random sample consisted of 41people who had been charged with drunken driving. During a telephone interview, 23 of these responded accurately to the question asking if they had been charged with drunken driving during the past 12 months. Assume the samples are representative of all people recently charged with drunken driving.

(a) Categorize the problem below according to parameter being estimated, proportion p, mean μ, difference of means μ₁ – μ₂, or difference of proportions p₁ – p₂. Then solve the problem.

μ₁ – μ₂p     p₁ – p₂μ

(b) Let p₁ represent the population proportion of all people with recent charges of drunken driving who respond accurately to a face-to-face interview asking if they have been charged with drunken driving during the past 12 months. Let p₂ represent the population proportion of all people who respond accurately to the question when it is asked in a telephone interview. Find a 99% confidence interval for p₁ – p₂. (Use 3 decimal places.)

(c) Does the interval found in part (a) contain numbers that are all positive? all negative? mixed? Comment on the meaning of the confidence interval in the context of this problem. At the 99% level, do you detect any differences in the proportion of accurate responses to the question from face-to- face interviews as compared with the proportion of accurate responses from telephone interviews?

Because the interval contains only positive numbers, we can say that there is a higher proportion of accurate responses in face-to-face interviews.Because the interval contains both positive and negative numbers, we can not say that there is a higher proportion of accurate responses in face-to-face interviews.     We can not make any conclusions using this confidence interval.Because the interval contains only negative numbers, we can say that there is a higher proportion of accurate responses in telephone interviews.

For the 2015 General Social Survey, a comparison of females and males on the number of hours a day that the subject watched TV gave the following results.

(a) Set up the hypotheses of a significance test to analyze whether the population means differ for females and males.

(b) Conduct all parts of the significance test if df = 499 and standard error = 0.163 . Interpret the P-value, and report the conclusion for α = 0.05.

(c) Conclusion

There is evidence that females, on average, watch more TV than males.There is not enough evidence to conclude that there is a gender difference in TV watching.    There is evidence to conclude that there is a gender difference in TV watching.

(d) If you were to construct a 95% confidence interval comparing the means, would it contain 0?

No, because according to the test 0 is a plausible value for the difference between the population means.Yes, because according to the test 0 is not a plausible value for the difference between the population means.    Yes, because according to the test 0 is a plausible value for the difference between the population means.No, because according to the test 0 is not a plausible value for the difference between the population means.

When choosing between two alternative regression models for the same data, what criteria should be used to select the best model?

A student wants to compare textbook prices for two online bookstores. She takes a random sample of five textbook titles from a list provided by her college bookstore, and then she determines the prices of those textbooks at each of the two websites. The prices of the five textbooks selected are listed below in the same order for each online bookstore.

A.com: $115, $43, $99, $80, $119

B.com: $110, $40, $99, $69, $109

(a) Are these independent or dependent samples?

Independent. The same textbooks are being compared.Dependent. The same textbooks are being compared.    Independent. Different textbooks are being compared.Dependent. Different textbooks are being compared.

(b) To construct a confidence interval, conditions for the data must be checked. Which variable should be checked?

the difference between the textbook price from A.com and the textbook price from B.com for each textbook.the prices of textbooks from B.com    the prices of textbooks from A.comthe difference between the average textbook price for A.com and the average textbook price for B.com

(c) Find a 94% confidence interval for the mean difference in textbook prices at the two online bookstores. (Use d = A.com - B.com.) HINT: Use StatCrunch. Enter the two columns of numbers, Stat > t stat > choose the appropriate test and fill in what's needed (   ,   ) (Use 3 decimal places)

(d) Suppose conditions are met. Using α = 0.06, is there evidence to indicate that the mean price of textbooks for A.com differs from the mean price of textbooks for B.com?

Because the interval does not contain zero, it is not plausible that the mean difference between A.com and B.com is 0. There is evidence to indicate that the mean price of textbooks for A.com is different from the mean price of textbooks for B.com .Because the interval contains zero, it is not plausible that the mean difference between A.com and B.com is 0. There is evidence to indicate that the mean price of textbooks for A.com is different from teh mean price of textbooks for B.com.    Because the interval does not contain zero, it is plausible that the mean difference between A.com and B.com is 0. There is not enough evidence to indicate that the mean price of textbooks for A.com is different from the mean price of textbooks for B.com.Because the interval contains zero, it is plausible that the mean difference between A.com and B.com is 0. There is not enough evidence to indicate that the mean price of textbooks for A.com differs from the mean price of textbooks for B.com.

Two best friends sell cupcakes. They have 3 boxes red velvet , 5 boxes vanilla, 4 boxes chocolate, and 6 peanut butter. Each box they sells for $4.

a)   Define random variable
b)   Determine probability distribution and parameters for the random variable defined in item a.
c)   Suppose that after two hours ten boxes of cupcakes have been purchased. Determine the cumulative distribution function for the number of red velvet purchased
d)   Draw the probability distribution function for the number of red velvet purchased.

Find P(Z ≥ 1.8). Round answer to 4 decimal places.

John runs a computer software store. Yesterday he counted 139 people who walked by the store, 62 of whom came into the store. Of the 62, only 22 bought something in the store.

(a) Estimate the probability that a person who walks by the store will enter the store. (Round your answer to two decimal places.)


(b) Estimate the probability that a person who walks into the store will buy something. (Round your answer to two decimal places.)


(c) Estimate the probability that a person who walks by the store will come in and buy something. (Round your answer to two decimal places.)


(d) Estimate the probability that a person who comes into the store will buy nothing. (Round your answer to two decimal places.)

Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean μ = 6350 and estimated standard deviation σ = 2000. A test result of x < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection.

(a) What is the probability that, on a single test, x is less than 3500? (Round your answer to four decimal places.)


(b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x?

a) The probability distribution of x is approximately normal with μ_x = 6350 and σ_x = 2000.

b) The probability distribution of x is approximately normal with μ_x = 6350 and σ_x = 1000.00.    

c) The probability distribution of x is approximately normal with μ_x = 6350 and σ_x = 1414.21.

d) The probability distribution of x is not normal.

What is the probability of x < 3500? (Round your answer to four decimal places.)


(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)

(d) Compare your answers to parts (a), (b), and (c). How did the probabilities change as n increased?

a) The probabilities decreased as n increased.

b)The probabilities stayed the same as n increased.  

c) The probabilities increased as n increased.

If a person had x < 3500 based on three tests, what conclusion would you draw as a doctor or a nurse?

a) It would be an extremely rare event for a person to have two or three tests below 3,500 purely by chance. The person probably has leukopenia.

b) It would be an extremely rare event for a person to have two or three tests below 3,500 purely by chance. The person probably does not have leukopenia.

c) It would be a common event for a person to have two or three tests below 3,500 purely by chance. The person probably has leukopenia.

d) It would be a common event for a person to have two or three tests below 3,500 purely by chance. The person probably does not have leukopenia.

Bark beetles are tiny insects with hard, cylindrical bodies that reproduce under the bark of trees. While bark beetles are native to U.S. forests and play important ecological roles, they can cause extensive tree mortality and negative economic and social impacts. Researchers at Los Alamos National Laboratory are interested in the behavior of Bark Beetles living in the Santa Fe National Forest. In particular, they are interested in the average size of these beetles (body length measured in mm). They assume that the distribution of body length for these beetles can be modeled with a Normal distribution with mean μ and standard deviation σ. After spending several weeks in the field, they have measured and recorded the body length of 263 of these beetles. The average body length of these 263 beetles is 6.14mm with a calculated standard deviation of 1.89mm.

1. What is the population of interest?

2. What is the sample size?

3. What is the sample?

4. What parameters are mentioned in this problem? Explain what the parameters mean in terms of the problem.

5. What is the sample data?

6. What are the estimators mentioned in this problem? For each estimator, explain which parameter it is supposed to estimate.

7. What are the estimates for the parameters in this problem?

The data presented in the table below resulted from an experiment in which seeds of 4 different types were planted and the number of seeds that germinated within 4 weeks after planting was recorded for each seed type.

At the .05 level of significance, is the proportion of seeds that germinate dependent on the seed type?

• A.

  No, the proportion of seeds that germinate are not dependent on the seed type because the p-value = 0.0132.

• B.

  No, the proportion of seeds that germinate are not dependent on the seed type because the p-value = 0.0265.

• C.

  Yes, the proportion of seeds that germinate dependent on the seed type because the p-value = 0.0265.

• D.

  Yes, the proportion of seeds that germinate dependent on the seed type because the p-value = 0.0132.