Triple A Battery Company is a major battery manufacturer of batteries and it produces three types of batteries (Type A, B, and C). The batteries are similar in construction but carry a different warranty period. Type A has a 36 month warranty, Type B has a 48 month warranty, and Type C has a 60 month warranty. Regardless of the warranty period, the standard deviation of a battery’s life is 2.5 months. Let’s consider the 36 month battery (Type A) for the following questions.

1. If the average life of a Type A battery is 38 months, then what proportion of the batteries will fail before the warranty period?
2. If a Type A battery is chosen at random, what is the probability that battery will last at least 42 months? Assume the mean life time of the battery is 38 months.
3. Each year, the company establishes a budget for warranty costs. If a battery does not last until the warranty period expires, then they have to replace the battery at no charge to the customer. This year they expect to replace 2% of the Type A batteries. What is the cutoff point, in months, for this 2%?
4. Given the scenario in the previous problem, what would the mean lifetime have to be for the company to stay under budget for the Type A batteries? In other words, what would the mean have to be if only 2% of the population is less than 36 months?
5. The company has found that if their Type A batteries last at least 6 months beyond the warranty period (44 months or more), then the customer is sure to buy their battery as a replacement when it fails. What portion of the customers can they count on as being repeat customers? Assume the mean life is 38 months.

Students' heights from Dorm A are normally distributed with a mean of 69.4 inches and standard deviation of 1.8 inches. Students heights from Dorm B are normally distributed with a mean of 71.6 inches and standard deviation of 1.7 inches. (You may consider these all to be population data.) A student is selected from one of the two dorms, but you don't know which one. At least how tall would that student need to be to have a probability of less than 0.03 of being from Dorm A? Round your answer to the second decimal place. If you cannot find the exact table entry you are looking for, use the value closest to the one you need. If there's a tie, use the smaller of the two possible entries.

please give step by step instructions on solution. The answer is 72.78 but im not sure how to do it.

If T₁ and T₂ are independent exponential random variables, find the density function of R=T₍₂₎ - T₍₁₎.

This is for the difference of the order statistics not of the variables, i.e. we are not looking for T₂ - T₁. It is implied that they are both from the same distribution. I know that

f_T(t) = λe^-λt

f_T(1)T(2)(t₁,t₂) = 2 f_T(t₁)f_T(t₂) = 2λ² e^{-λ​​​​​​​t₁} e^{-λ​​​​​​​t₂} , 0 < t₁ < t₂ and I need to find f_R(r).

From Mathematical Statistics and Data Analysis by Rice, 3rd Edition, Question 79 from Chapter 3. The solution in the back of the book: "Exponential (λ)". I am not sure how to get to that answer.

Two states of nature exist for a particular situation: a good economy and a poor economy. An economic study may be performed to obtain more information about which of these will actually occur in the coming year. The study may forecast either a good economy or a poor economy. Currently there is a 60% chance that the economy will be good and a 40% chance that it will be poor. In the past, when ever the economy was good, the economic study predicted it would be good 80% of the time. (The other 20% of the time the prediction was wrong.) In the past, whenever the economy was poor, the economic study predicted it would be poor 90% of the time. (The other 10% of the time the prediction was wrong.)

(A) Use Bayes’ theorem and find the following:

P (good economy | prediction of good economy)

P (poor economy | prediction of good economy)

P (good economy | prediction of poor economy)

P (poor economy | prediction of poor economy)

(B) Suppose the initial (prior) probability of a good economy is 70% (instead of 60%), and the probability of a poor economy is 30% (instead of 40%). Find the posterior probabilities in part a

based on these new values.

Suppose that the distribution of scores on an exam is mound shaped and approximately symmetric. The exam scores have a mean of 110 and the 16th percentile is 85. (Use the Empirical Rule.)

(a)

What is the 84th percentile?

(b)

What is the approximate value of the standard deviation of exam scores?

(c)

What is the z-score for an exam score of 90?

(d)

What percentile corresponds to an exam score of 160?

%

(e)

Do you think there were many scores below 35? Explain.

Since a score of 35 is  ---Select--- one standard deviation two standard deviations  three standard deviations  below the mean, that corresponds to a percentile of  %. Therefore, there were  ---Select--- many few scores below 35.

The use of correlation statistics in clinical practice

A university believes that the average retirement age among the faculty is now 70 instead of the historical value of 65. A sample of 35 faculty found that the average of their expected retirement age is 68.4 with a standard deviation of 3.6. Conduct the appropriate hypothesis test to determine if the mean retirement age is not equal to 70.

Round your final answer to four decimal places. 0.0000

9. ANCOVA assumptions also require that the regression slopes for a covariate are homogeneous. T F

10. The sixth assumption for ANCOVA is that the covariate is reliable and is measured without error. T F

11. The assumption of homogeneity of variances is best tested through the use of Levine’s test. T F

12. The assumption of linearity is more precisely tested by obtaining and examining residual plots between the covariates and the IVs. T F

13. Regression is incorporated into ANCOVA in order to predict scores on the DV based on knowledge of scores on the covariate. T F

14. A violation of the assumption of homogeneous regression slopes is crucial with respect to the validity of the results of ANCOVA. T F

15. The null hypothesis being tested with the assumption of homogeneity of regression slopes is that all regression slopes are equal. T F

16. The logic of ANCOVA is identical to the logic behind ANOVA. T F

Question with regards to Statistical Process Control.

Control chart systems can operate on two basic methods of measurement. State these two methods and briefly distinguish between them, giving three examples of industrial processes where each might be applied. Specify an appropriate sampling procedure in each case.

When someone buys a ticket for an airline​ flight, there is a 0.0973 probability that the person will not show up for the flight. A certain jet can seat 17 passengers. Is it wise to book 19 passengers for a flight on the​ jet? Explain. Determine whether or not booking 19 passengers for 17 seats on the jet is a wise decision. Select the correct choice below and fill in the answer box in that choice with the probability that there are not enough seats on the jet. ​(Round to four decimal places as​ needed.)

In a study of credibility or believability of television news versus printed news, a sample of 35 adults was selected from residents of an urban area in the Midwest. Each person was asked to express his or her opinion regarding the statement “Television news is more trustworthy than corresponding news reported in the printed media.” Responses were measured on a five-point scale from “strongly agree” (1) to “Strongly Disagree” (5), and were reported as follows:

4 4 3 5 5 3 5 2 4 1 4 1 3 4 3 4 5 5 5 5 5 4 4 3 2 5 1 5 4 5 4 2 3 4 4

1. Construct a frequency distribution table that corresponds to this data and draw a frequency graph of the distribution
2. Calculate the mean, median, mode, range, variance, and standard deviation (Show ALL work for Standard Deviation legibly).

Thank you!

According to a study done by a university​ student, the probability a randomly selected individual will not cover his or her mouth when sneezing is

0.2670.267.

Suppose you sit on a bench in a mall and observe​ people's habits as they sneeze.

​(a) What is the probability that among

1818

randomly observed individuals exactly

55

do not cover their mouth when​ sneezing?

​(b) What is the probability that among

1818

randomly observed individuals fewer than

33

do not cover their mouth when​ sneezing?

​(c) Would you be surprised​ if, after observing

1818

​individuals, fewer than half covered their mouth when​ sneezing? Why?

USING EXCEL FORMULAS SOLVE THE PROBLEM. MUST USE EXCEL CALCULATIONS AND FORMULAS.!!!

1. Find the data for the problem in the first worksheet named LightbulbLife of the data table down below It gives the data on the lifetime in hours of a sample of 50 lightbulbs. The company manufacturing these bulbs wants to know whether it can claim that its lightbulbs typically last more than 1000 burning hours. So it did a study.
   1. Identify the null and the alternate hypotheses for this study.
   2. Can this lightbulb manufacturer claim at a significance level of 5% that its lightbulbs typically last more than 1000 hours? What about at 1%? Test your hypothesis using both, the critical value approach and the p-value approach. Clearly state your conclusions.
   3. Under what situation would a Type-I error occur? What would be the consequences of a Type-I error?
   4. Under what situation would a Type-II error occur? What would be the consequences of a Type-II error?

In one population, it is found that 6% of all people have high blood pressure and 40% are overweight. Four percent suffer from both con- ditions. What is the probability that a randomly selected person from this population will have high blood pressure given that he is not over- weight?

Please explain :)

Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 19 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with σ = 0.26 gram.

(a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.)

(b) What conditions are necessary for your calculations? (Select all that apply.)

σ is knownσ is unknownnormal distribution of weightsn is largeuniform distribution of weights

(c) Interpret your results in the context of this problem.

The probability to the true average weight of Allen's hummingbirds is equal to the sample mean.The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.    There is an 80% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.There is a 20% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20.

(d) Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.15 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)
hummingbirds