Confidence interval for mean

1) A food inspector, examining 5 jars of a certain brand of peanut butter, obtained the following percentages of impurities:
2.3; 1.9; 2.1; 2.8; 2.3
Assuming that such determinations are normally distributed, construct a 99% confidence interval for the average percentage of impurities in this brand of peanut butter.

2) Twelve randomly selected citrus trees of one variety have a mean height of 13.8 ft with a standard deviation of 1.2 feet, and fifteen randomly selected citrus trees of another variety have a mean height of 12.9 ft with a standard deviation of 1.5 ft. Stating appropriate assumptions, construct a 95% confidence interval for the difference between the true average heights of the two kinds of citrus trees.

3) A box contains 500 ball bearings which have a mean weight of 5.02 ounces and a standard deviation of 0.3 ounces. A random sample of 100 ball bearings is drawn with replacement from that box. Let x- be the mean weight of the sample of 100 ball bearings. Estimate the probability that x- will be between 4.96 and 5.00 ounces.

4) In a random sample of 120 cheerleaders, 54 suffered moderate to severe damage to their voices. Find a 90% confidence interval for the true proportion of cheerleaders who are afflicted in this way.

5)Miss Prim’s class of grade 1 students has 22 children whose mean height is 47.75 inches while Mr. Trim’s class of grade 2 students has 25 children whose mean height is 50.4 inches. The standard deviations of the heights of first graders and second graders are known in general to be 1.8 inches and 2.05 inches, respectively. Stating appropriate assumptions, find a 98% confidence interval for the mean growth µ2 -µ1 between second graders and first graders.

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