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Question: A machine at K&A Tube & Manufacturing


A machine at K&A Tube & Manufacturing Company produces a certain copper tubing component in a refrigeration unit. The tubing components produced by the manufacturer have a mean diameter of 0.75 inch with a standard deviation of 0.004 inch. The quality-control inspector takes a random sample of 30 components once each week and calculates the mean diameter of these components. If the mean is either less than 0.748 inch or greater than 0.752 inch, the inspector concludes that the machine needs an adjustment.
(a) Describe the sampling distribution of /, the sample mean diameter, for a random sample of 30 such components.
(b) What is the probability that, based on a random sample of 30 such components, the inspector will conclude that the machine needs an adjustment when, in fact, the machine is correctly calibrated?


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>  = 70,  = 10, P(65 < X < 85)

>  = 30,  = 5, P(X ≤ 23)

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> Length (in minutes) of a country song

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> A random sample of 1005 adult Americans was asked, “How would you prefer to pay for new road construction?” Results of the survey are below. (a) Construct a relative frequency distribution. (b) What percent of the respondents indicated they would like to

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> The graph shows the ratings on Yelp for Hot Doug’s Restaurant. (a) Which was the most popular rating for Hot Doug’s? (b) How many ratings were posted on Hot Doug’s? (c) How many more 5 Star ratings are there than 4 Star ratings? (d) What percentage of ra

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> Explain the difference between a lurking variable and a confounding variable.

> The area to the left of z = -1.04.

> Researchers Katherine Tucker and associates wanted to determine whether consumption of cola is associated with lower bone mineral density. They looked at 1125 men and 1413 women in the Framingham Osteoporosis Study, which is a cohort that began in 1971.

> A pharmaceutical company has developed an experimental drug meant to relieve symptoms associated with the common cold. The company identifies 300 adult males 25 to 29 years old who have a common cold and randomly divides them into two groups. Group 1 is

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> A continuous random variable X is uniformly distributed with / (a) Draw a graph of the uniform density function. (b) What is / (c) What is /

> Does the shape of a glass play a role in determining the amount of time it takes to finish the drink? Researchers identified 159 male and female self- professed social drinkers. One week the subjects were given a 12 ounce beer with either a straight g

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> Use the results in the table to (a) draw a normal plot, (b) determine the linear correlation between the observed values and expected z-scores, (c) determine the critical value in Table VI to assess the normality of the data.

> A school psychologist wants to test the effectiveness of a new method for teaching reading. She recruits 500 first-grade students in District 203 and randomly divides them into two groups. Group 1 is taught by means of the new method, while group 2 is ta

> A casino manager wants to inspect a sample of 14 slot machines in his casino for quality-control purposes. There are 600 sequentially numbered slot machines operating in the casino. Obtain a systematic sample of 14 slot machines. Be sure to discuss how y

> According to a Gallup poll, 46% of Americans 18 years old or older stated that they had read at least six books (fiction and nonfiction) within the past year. You conduct a random sample of 250 Americans 18 years old or older and ask the individuals to d

> A farmer has a 500-acre orchard in Florida. Each acre is subdivided into blocks of 5. Altogether, there are 2500 blocks of trees on the farm. After a frost, he wants to get an idea of the extent of the damage. Obtain a sample of 10 blocks of trees using

> According to Major League Baseball rules, the ball must weigh between 5 and 5.25 ounces. A factory produces baseballs whose weights are approximately normally distributed, with mean 5.11 ounces and standard deviation 0.062 ounce. Source: www.baseball-alm

> A congresswoman wants to survey her constituency regarding public policy. She asks one of her staff members to obtain a sample of residents of the district. The frame she has available lists 9012 Democrats, 8302 Republicans, and 3012 Independents. Obtain

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