11.a quart of Parker’s milk contains a mean of 39 grams of butterfat, with a standard deviation of 2 grams. If the butterfat is normally distributed, find the probability that a quart of this brand of milk chosen at random will contain between:

(a) 39 and 43 grams of butterfat

(a) 36 and 39 grams of butterfat

12.The Scholastic Aptitude Test (SAT) scores in mathematics at a certain high school are normally distributed, with a mean of 500 and a standard deviation of 100. What is the probability that an individual chosen at random has a score:

(a)greater than 700?

(b)Less than 300?

(c)Between 550 and 600?

How do I do these? I have a test on these tommorow and I have no idea how to do them. Please help me!

Your textbook should have tables for standard deviation. You need to understand how to use them for your test. Translate the word problems into how many standard deviations above or below the mean. Combining that with reading the tables is all you need for now.

11a) The question is really what is the probability of a result between the mean (39) and two standard deviations above the mean (39 + 2 + 2). Your table should show you that is 50% and approximately 97.7%, so the amount between is 97.7 – 50 = 47.7%

11b) What is the probability of an answer between 1.5 standard deviations below the mean (39 – 1.5*2) and the mean (39)? You should be able to read that from your table.

12a and 12b have the same answer. The probability of a score more than two standard deviations above the mean (500 + 100*2) is the same as the probability of a score two standard deviations below the mean (500 – 100*2). Approx 2.3% in each case.

12c) 550 is 1/2 standard deviation above the mean. 600 is 1 sdev above. That’s all the info you need to use the tables.

Hope that helps.