1) The extract of a plant native to Taiwan has been tested. One of the chemical compounds produced from the plant was analyzed for a particular collagen. The collagen amount was found to be normally distributed with a mean of 68 and a standard deviation of 6.1 grams per milliliter.
(a) What is the probability that the amount of collagen is greater than 62 grams per milliliter?
(b) What is the probability that the amount of collagen is less than 74 grams per milliliter?
(c) What percentage of compounds formed from the extract of this plant fall within 1 standard deviation of the mean?
2) An automobile insurer has found that repair claims are Normally distributed with a mean of $920 and a standard deviation of $860.
(a) Find the probability that a single claim, chosen at random, will be less than $900.
(b) Now suppose that the next 90 claims can be regarded as a random sample from the long-run claims process. Find the probability that the average of the 90 claims is smaller than $900.
3) A random sample of n measurements was selected from a population with a standard deviation σ= 18.1 and an unknown mean. Calculate a µ= 90% confidence interval for each of the following situations:
(a) n = 55, x = 76.5
(b) n = 80, x = 76.5
(c) n = 95, x = 76.5