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1. Items produced by a manufacturing process are supposed to weigh 90 grams. The distribution of weights can be approximated by a Normal distribution with a standard deviation of 1 gram. Using the Empirical Rule: about what percentage of the items will either weigh less than 87 grams or more than 93 grams? 2. Birthweights at a local hospital have a Normal distribution with a mean of 110 oz. and a standard deviation of 15 oz. Using the Empirical Rule: what is the proportion of infants with birthweights above 95 oz.? 3. Suppose that scores on a certain IQ test are Normally distributed with a mean of 110 and standard deviation of 15. Then about 60% of the scores are between: a. 97 and 123 b. 95 and 118 c. 80 and 140 d. 65 and 155 4. If the heights of 99.7% of American cars have fuel economy between 19 and 34 miles per gallon, what is your estimate of the standard deviation of the fuel economy? 5. The scores on a university examination are Normally distributed with a mean of 62 and a standard deviation of 11. If the bottom 5% of students will fail the course, what is the lowest mark that a student can have and still be awarded a passing grade? 6. A company produces packets of soap powder that are labeled "Giant Size 32 Ounces." The actual weight of soap powder in a box has a Normal distribution with a mean of 33 oz. and a standard deviation of 0.7 oz. 95% of packets actually contain more than x oz. of soap powder. What is x? 7. A company produces packets of soap powder that are labeled "Giant Size 32 Ounces." The actual weight of soap powder in a box has a Normal distribution with a mean of 33 oz. and a standard deviation of 0.7 oz. What is the probability that a box of 36 packets has a mean weight less than 32.8 oz? 8. It was found that the mean length of 100 parts produced by a lathe was 20.05 mm with a standard deviation of 0.02 mm. Find the probability that a part selected at random would have a length between 20.05 and 20.08 mm. 9. It was found that the mean length of 100,000 parts produced by a lathe was 20.05 mm with a standard deviation of 0.2 mm. Jerry, the QC inspector, finds a package of 100 parts to have a mean of 20.08 mm. Find the probability of getting a package with the mean of 20.08 mm or higher. 10. A fire department in a rural county reports that its response time to fires is approximately Normally distributed with a mean of 22 minutes and a standard deviation of 11.9 minutes. Approximately what proportion of their response times is over 30 minutes?

1. Items produced by a manufacturing process are supposed to weigh 90 grams. The distribution of weights can be approximated by a Normal distribution with a standard deviation of 1 gram. Using the Empirical Rule: about what percentage of the items will either weigh less than 87 grams or more than 93 grams?
2. Birthweights at a local hospital have a Normal distribution with a mean of 110 oz. and a standard deviation of 15 oz. Using the Empirical Rule: what is the proportion of infants with birthweights above 95 oz.?
3. Suppose that scores on a certain IQ test are Normally distributed with a mean of 110 and standard deviation of 15. Then about 60% of the scores are between:
a. 97 and 123
b. 95 and 118
c. 80 and 140
d. 65 and 155
4. If the heights of 99.7% of American cars have fuel economy between 19 and 34 miles per gallon, what is your estimate of the standard deviation of the fuel economy?
5. The scores on a university examination are Normally distributed with a mean of 62 and a standard deviation of 11. If the bottom 5% of students will fail the course, what is the lowest mark that a student can have and still be awarded a passing grade?
6. A company produces packets of soap powder that are labeled "Giant Size 32 Ounces." The actual weight of soap powder in a box has a Normal distribution with a mean of 33 oz. and a standard deviation of 0.7 oz. 95% of packets actually contain more than x oz. of soap powder. What is x?
7. A company produces packets of soap powder that are labeled "Giant Size 32 Ounces." The actual weight of soap powder in a box has a Normal distribution with a mean of 33 oz. and a standard deviation of 0.7 oz. What is the probability that a box of 36 packets has a mean weight less than 32.8 oz?
8. It was found that the mean length of 100 parts produced by a lathe was 20.05 mm with a standard deviation of 0.02 mm. Find the probability that a part selected at random would have a length between 20.05 and 20.08 mm.
9. It was found that the mean length of 100,000 parts produced by a lathe was 20.05 mm with a standard deviation of 0.2 mm. Jerry, the QC inspector, finds a package of 100 parts to have a mean of 20.08 mm. Find the probability of getting a package with the mean of 20.08 mm or higher.
10. A fire department in a rural county reports that its response time to fires is approximately Normally distributed with a mean of 22 minutes and a standard deviation of 11.9 minutes. Approximately what proportion of their response times is over 30 minutes?

Added by Dominique B.

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