## (CORRECT ANSWER) MATH225N Week 6 Assignment : Confidence Intervals-Empirical Rule

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**Question**

The average length of an eel from a population of short-finned eels is unknown. A random sample from the population yields a sample mean of x¯=1.9 feet. Assume the sampling distribution of the mean has a standard deviation of σx¯=0.6 feet.

Use the Empirical Rule to construct a 95% confidence interval for the true population mean length.

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**Question**

In a survey, a random sample of adults were asked whether a tomato is a fruit or vegetable. The survey resulted in a sample proportion of p′=0.58, with a sampling standard deviation of σp′=0.08, who stated a tomato is a fruit.

Write a 99.7% confidence interval for the true proportion of adults who stated a tomato is a type of fruit.

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**Question**

The average number of onions needed to make French onion soup from a population of recipes is unknown. A random sample of recipes yields a sample mean of x¯=8.2 onions. Assume the sampling distribution of the mean has a standard deviation of σx¯=2.3 onions.

Use the Empirical Rule to construct a 95% confidence interval for the true population mean number of onions.

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**Question**

In a random sample of 30 young bears, the average weight at the age of breeding is 312 pounds. Assuming the population ages are normally distributed with a population standard deviation is 30 pounds, use the Empirical Rule to construct a 68% confidence interval for the population average of young bears at the age of breeding. Do not round intermediate calculations. Round only the final answer to the nearest pound. Remember to enter the smaller value first, then the larger number.

Ans.

**Question**

A random sample of garter snakes were measured and the proportion of snakes that were longer than 20 inches in length recorded. The measurements resulted in a sample proportion of p′=0.25, with a sampling standard deviation of σp′=0.05.

Write a 68% confidence interval for the true proportion of garter snakes that are over 20 inches in length.

Ans.

**Question**

The average height of a population is unknown. A random sample from the population yields a sample mean of x¯=66.3 inches. Assume the sampling distribution of the mean has a standard deviation of σx¯=0.8 inches.

Use the Empirical Rule to construct a 95% confidence interval for the true population mean height.

Ans.

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