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Consider an inventory system in which the sequence of events during each period is as follows. (1) We observe the inventory level (call it i) at the beginning of the period.
We roll two six sided dice, one with sides 1,2,2,3,3,4 and the other with sides 1,3,4,5,6,8. What is the distribution of the sum?
Suppose that you add 10 to all of the observations in a sample. How does this change the sample mean? How does it change the sample standard deviation?
Construct a relative frequency distribution for each car type. Draw a side-by-side relative frequency bar graph. Compare the colors for the two car types. Make a conjecture about the reasons for the d
When a certain manufacturing process is correctly adjusted, the length of a machine part produced is a random variable with a mean of 200 cm and a standard deviation of 0.1 cm. The individual meas
At the 5% level of significance, test that the percentage of defective printed circuit boards is 10% against the alternative that it is greater than 10%. Find the p-value for the test.
Why is it important that a sample be random? For its validity, all hypothesis testing depends heavily on the assumption that the sample that is used was drawn using probability sampling techniques.
A company that produces an expensive stereo component is considering offering a warranty on the component. Suppose the population of life-times of the components is a normal distribution with a mean
The following are the numbers of defective parts produced in a shift by 10 workers before and after going through a very rigorous training program:
To minimize the number of bulbs that burn out during operating hours, all bulbs are replaced at once. How often should the bulbs be replaced so that no more than 1% burn out between replacement peri
Assuming (approximately) normal distributions having equal variances for percent wear of tires of each brand under these test conditions, find a 95% confidence interval for \(\mu_{A}-\mu_{B}\)
What is the point estimate of the population mean planting time? What is the 99% interval estimate for the population mean planting time?
You run an advertising company and need to know how much time per day an average person spends listening to the radio. You want to be within 4 minutes of the population mean listening time w
Which statistical analysis technique should be used? What is the null hypothesis? Can an analysis be performed? Why or why not?
Which statistical analysis technique should be used? What is the null hypothesis? Can the market researcher get an answer? Why or why not?
Let X denote a geometric random variable with parameter p. For s >=0, compute E[e^(-sX)]. For what other values of s is your calculation valid?
You and your opponent both roll a fair die. If you both roll the same number, the game is repeated otherwise whoever rolls the larger number wins. Let N be the number of times the two dice have to
Using D to denote the event that the selected household has a dog and C to denote the event that the selected household has a cat, symbolically denote the following events and identify the number of
The supplier has determined that the standard deviation of its production process is 0.05 cm. The process is normally distributed. Each of the following questions is independent except question e wh
On a normal distribution with a mean of 500 and a standard deviation of 97, what percentage of cases will fall between 470 and 550?
Which of these variables are categorical and which are quantitative? Give the units for the quantitative variables and the categories for the categorical variables. What are the individuals in the r
A box contains n marbles each of which is labeled (by engraving) by one of the integers 1, 2, . . . , n. Two of the marbles are drawn in succession without replacement. Let X and Y denote the intege
A survey of adults found that 55% have used a multivitamin in the past 12 months. You randomly select 50 adults and ask them if they have used a multivitamin in the past 12 months. If this is a bin
Given a pair of fair dice (each face is equally likely to show upward). What is the expectation of this random variable (the summation of the two numbers showing upward)?
A study investigated how the size of a person's dwelling was related to their ownership of motor vehicles. They found that dwelling size and number of vehicles owned was strongly correlated and conc