Laptops produced by a company last on an average of 5 years. The life span of each laptop follows an exponential distribution.

            (6). What is the probability that a laptop will last in less than 3 years?

            (7). What is the probability that a laptop will have the life span at least 10 years?

(8). How many laptops from 1000, would be expected to work between 4 and 7 years? (Choose the nearest integer).

Questions 28-29: You have collected data on heights, in inches, from 41 males and 52 females. The sample standard deviations for males and females are, respectively, 6.1 and 4.9.

28. Find the appropriate test statistic to test equality of variances between the genders.: *
(A) 0.2541
(B) 1.2449
(C) 1.5498
(D) 7.5939

29. On what distribution would you obtain the p-value?: *
(A) The F distribution with degrees of freedom 41 and 52.
(B) The T distribution with degrees of freedom 91.
(C) The T distribution with degrees of freedom 40.
(D) The chi-square distribution with degrees of freedom 1.
(E) The F distribution with degrees of freedom 40 and 51.

30. You conduct a two-tailed hypothesis test, which turns out to be significant at α = 0.03. A corresponding confidence interval for the same test would have what confidence?: *
(A) 3%
(B) 95%
(C) 97%
(D) 97.5%

6. All of the following statements about confidence intervals are correct EXCEPT?: *
(A) Holding other numbers fixed, increasing the level of confidence will result in a wider confidence interval.
(B) Holding other numbers fixed, increasing sample size will result in a narrower confidence interval.
(C) The sample mean / proportion will always be inside the confidence interval.
(D) The population mean / proportion will always be inside the confidence interval.

7. Weight, in pounds, is measured for each person in a sample. After the data are collected, all the weight measurements are converted from pounds to kilograms by multiplying each measurement by 2.2. Which of the following statistics will remain the same for both units of measure?: *
(A) The z-scores of the weight measurements.
(B) The maximum of the weight measurements.
(C) The standard deviation of the weight measurements.
(D) The median of the weight measurements.
(E) The mean of the weight measurements.

8. The weight of a carton of strawberries has mean of 16 ounces and standard deviation of 1.5 ounces. What can you say about the distribution of the mean weight of a random sample of 41 cartons?: *
(A) Mean = 16, standard error = 1.5, unknown shape
(B) Mean = 16, standard error = 1.5, approximately normal
(C) Mean = 16, standard error = 0.234, unknown shape
(D) Mean = 16, standard error = 0.234, approximately normal

The police that patrol a heavily traveled highway claim that the average driver exceeds the 65 miles per hour speed limit by more than 10 miles per hour. Seventy-two randomly selected cars were clocked by airplane radar. The average speed of the 72 cars was 77.40 miles per hour, and the standard deviation of these speeds was 5.90 miles per hour. Test a 5% level of significance whether the average speed by all drivers is more than 75 mph. Make sure to show all of your work and include every step.

The manufacturer of an MP3 player wanted to know whether a 10% reduction in price is enough to increase the sales of its product. To investigate, the owner randomly selected eight outlets and sold the MP3 player at the reduced price. At seven randomly selected outlets, the MP3 player was sold at the regular price. Reported below is the number of units sold last month at the regular and reduced prices at the randomly selected outlets. Regular price 138 124 89 112 116 123 98 Reduced price 124 134 154 135 118 126 133 132 Click here for the Excel Data File . At the 0.025 significance level, can the manufacturer conclude that the price reduction resulted in an increase in sales? Hint: For the calculations, assume reduced price as the first sample.

Compute the pooled estimate of the variance. (Round your answer to 3 decimal places.)

Compute the test statistic. (Round your answer to 2 decimal places.)

State your decision about the null hypothesis. Reject H0 Fail to reject H0

The table below contains data on individual’s usage of a social media platform. It categorizes the data on the age range of the individual and their reported usage level. Use this table to answer the question that follows it.

What is the probability that a randomly selected individual reports a low usage level, a moderate usage level, or both?

You have been recording how many miles you get per tank of gas, and you have found a mean of 297 and a standard deviation of 23. Use this information to answer the following question.

What is the probability you will get 300 miles out of a tank of gas?

A population of values has a normal distribution with μ=195μ=195 and σ=3.7σ=3.7. You intend to draw a random sample of size n=230n=230.

Find the probability that a single randomly selected value is between 194.9 and 195.3.
P(194.9 < X < 195.3) =

Find the probability that a sample of size n=230n=230 is randomly selected with a mean between 194.9 and 195.3.
P(194.9 < ¯xx¯ < 195.3) =

Enter your answers as numbers accurate to 4 decimal places. Answers should be obtained using zz scores correct to two decimal places.

The university finance department wants to know if the average age of students at their university is greater than the average for other universities. A random sample of student records is taken from the own university (population 1) and a random selection of student ages from other three universities are taken (population 2). A significance level of 0.05 is chosen.

The null and alternative hypotheses are:

?0:

??:

The samples are selected, and the results are:

?1 = 28,7 ?????   ?1 = 5.1 ?????   ?1 = 125

?2 = 24,9 ?????   ?2 = 3.5 ?????   ?2 = 250

An urn contains five black marbles and one orange marbles. Four marbles are drawn out one at a time. For each marble, if it is black the marble is set aside, but if it is orange it is returned to the urn before the next marble is drawn. Let X be the number of black marbles drawn from the urn. Find the probability distribution for X and find the expectation value and variance of X

Pick three of the following control tools and identify situations where that particular tool might be useful:

1. EVM
2. Benchmarking
3. Critical Ratios

An agency offers preparation courses for a graduate school admissions test to students. As part of an experiment to evaluate the merits of the​ course, 40 students were chosen and divided into 20 pairs in such a way that the members of any pair had similar academic records. Before taking the​ test, one member of each pair was assigned at random to take the preparation​ course, while the other member did not take a course. The achievement test scores are contained in the accompanying table. Assuming that the differences in scores follow a normal​ distribution, test at the

1010​%

​level, the null hypothesis that the two population means are equal against the alternative that the true mean is higher for students taking the preparation course.

Let

mu 1μ1

be the mean test scores for those who took the preparation course and let

mu 2μ2

be the mean test scores for those who did not take the course. Determine the null and alternative hypotheses. Choose the correct answer below.

H0=?

H1=?

The test statistic is t=?

The critical​ value(s) is(are) =?

Determine the correct conclusion.

REJECT/DO NOT REJECT=? the null hypothesis since the test statistic is

BETWEEN -tn-1,a/2 and tn-1,a/2.  /LESS THAN -tn-1,a. / LESS THAN -tn-1,a/2.  /GREATER THAN tn-1,a/2.  /GREATER THAN -tn-1,a. /GREATER THAN tn-1,a.  /LESS THAN tn-1,a.=? There is SUFFİCİENT/UNSUFFİCİENT=? evidence that the true mean is higher for students taking the preparation

course.

ACHİEVEMENT TEST SCORES

UPPER CRİTİCAL VALUES OF STUDENT'S t DİSTRİBUTİON

I am trying to figure out the probability, expected value, variance, and standard deviation for a series of dice rolls. For example, if I roll a six-sided die in an attempt to roll a 1, and it takes me 7 rolls before a 1 appears, what are those answers? I have figured out the probability equation:

P(P-1)^x where x is the number of rolls - 1 so for 7 rolls the probability would be: 1/6(1-1/6)^6 = 0.05581632...

Further where I am lost is taking the above and using it to find the Expected Value, Variance, and Standard Deviation?

As I see the equations but plugging in numbers has me lost as p is the probability of failure and x = 0,1,2,3 for geometric distribution it would be

E(X)= (1-p)/p .... this is where I am lost as failure is 5/6 not 1/6 correct? Please show example of this so I can better understand, also on Variance, and Standard Deviation?

The town of Charlotte recently started a single-stream recycling program. The town provided 60-gallon recycling bins to 25 randomly selected households and 75-gallon recycling bins to 22 randomly selected households. The total volume of recycling over a 10-week period was measured for each of the households. The average total volumes were 382 and 415 gallons for the households with the 60- and 75-gallon bins, respectively. The sample standard deviations were 52.5 and 43.8 gallons, respectively. Assume that the 10-week total volumes of recycling are approximately normally distributed for both groups and that the population standard deviations are equal. Using a test statistic of -2.321 and a 2% significance level, can you conclude that the average 10-week recycling volume of all households having 60-gallon containers is different from the average volume of all households that have 75-gallon containers?

Then reconsider the town of Charlotte's recycling program. If we assume that the population standard deviations are different, we will have a test statistic of -2.348. We will also now have 44 degrees of freedom. Re-test the hypothesis given these calculations.

These are sample two population t-tests. Please show ALL the work up to the answers.

Find the 94th percentile, P₉₄,  from the following data

Please show work, I have tried to multiply total number of data points (36) by .94 percent to get the answer of 33.84, which I believe should be rounded to 34, leaving the logical answer to be 47.9 however this is NOT the correct answer.