Questions 27 through 29: A hot dog manufacturer asserts that one of its brands of hot dogs has an average fat content of 18 grams per hot dog. Fat contents in hot dogs from this manufacturer follow an approximately normal distribution with a standard deviation of 1.1 grams. Define the statistic to be $\bar{x}$ = mean fat content in a random sample of 10 hot dogs.
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Step 1: The population mean is $\mu = 18$ grams. Show more…
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a hot dog manufacturer asserts that one of its brands of hot dogs has an average fat content of 18 grams per hot dog. Fat contents in individual hot dogs from this manufacturer follow an approximately normal distribution with a standard deviation of 1.1 grams. Define the statistic x=mean fat content in a random sample of 10 hot dogs. A. Calculate the probability that fat content for a single randomly selected hot dog is less than 16 grams. Write the probability statement, the R code used, and the probability. B. What is the mean of the sampling distribution of x? C. What is the standard deviation of the sampling distribution of x? D. Explain why the sampling distribution of x is approximately normal. E. Calculate the probability that the average fat content in a random sample of 10 hot dogs is greater than 19.7 using the Z-scores. Write the probability statement, the R code used, and the probability.
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To find out how much fat is in a common hot dog, a nutritionist recorded the amount of fat per 100 grams of a random sample of 9 brands as follows: 4.5, 5, 5.75, 6, 6.75, 7, 7.25, 8, 8.25. Assume that the underlying distribution of fat in grams is normal. a. Find the mean and the standard deviation of the amount of fat. Round your answer to two decimal places. b. Find the 90% confidence interval for the average amount of fat in the hot dog. Round your answer to two decimal places.
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A manufacturer claims their brand of hot dogs have a mean fat content of 18 g with a standard deviation of 1 g. You will test random sample of 40 hot dogs for fat content. a. What is the probability that the mean fat content of the sample is over 18.25 g? b. What is the probability that the fat content of a single hot dog is over 18.25 g?
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