Math 141, Fall 2014, c Dr. Kamran Reihani - Texas A&M University
1. Calculate the following probabilities. ( Z is the standard normal random variable.)
(a) P (0 .
33 < Z < 0 .
47)
(b) P ( Z < 0 .
93)
(c) P ( Z > 0 .
29)
2. Find the value of z that satisfies the following probabilities.
(a) P ( Z < z ) = 0 .
3682
(b) P ( Z > z ) = 0 .
9778
(c) P ( − z < Z < z ) = 0 .
5254
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Math 141, Fall 2014, c Dr. Kamran Reihani - Texas A&M University
3. Suppose X is a normal random variable with µ = 380 and σ = 21.
Find the following probabilities.
(a) P ( X < 388)
(b) P (388 < X < 407)
(c) P ( X > 405)
4. Find the indicated quantities given that X is a normal random variable with a mean of 20 and a standard deviation of 4.
(a) Find the value of b such that P ( X ≤ b ) = 0 .
9463
(b) Find the value of c such that P ( X ≥ c ) = 0 .
6664
(c) Find the values of A and B such that P ( A ≤ X ≤ B ) = 0 .
9643 if A and B are symmetric about the mean.
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Math 141, Fall 2014, c Dr. Kamran Reihani - Texas A&M University
5. Suppose that the weights of students at a university are normally distributed with a mean of 165 pounds and a standard deviation 24 pounds. What is the probability that a student selected at random
(a) weighs between 150 and 200 pounds?
(b) weighs more than 215 pounds?
(c) What weight corresponds to the 85th percentile?
6. The government of a certain country wants to create a system for tax purposes where families are classified as “elite,” “upper class,” “middle class,” or “lower class” based on the total family income. Suppose family incomes in this country are normally distributed with a mean of $30,000 and a standard deviation of $9,000. If this government knows that they want 15% elite, 25% upper class, 40% middle class, and 20% lower class, what would be the range of income classified as “middle class?”
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Math 141, Fall 2014, c Dr. Kamran Reihani - Texas A&M University
7. The distribution of heights of adult males is normally distributed with mean 67 inches and standard deviation 2.7 inches. Answer the following. (Round your answers to 2 decimal places)
(a) What minimum height is taller than 68% of all adult males?
(b) What 2 heights that are symmetric about the mean enclose the middle 78% of all heights?
8. ( Applied Finite Mathematics , by E. Tomastik and J. Epstein) The length, in feet, of a certain structural steel beam is normally distributed with a mean of 10 feet and a standard deviation of 1 inch. Quality requirements demand a beam to be rejected if the length is more than 2 inches different from the mean. What percentage of the beams will be rejected? (Round your answer to two decimal places.)
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Math 141, Fall 2014, c Dr. Kamran Reihani - Texas A&M University
9. ( Applied Finite Mathematics , by E. Tomastik and J. Epstein) The number of ounces of detergent in an advertised one-pound box is normally distributed with a mean of 16.1 ounces and a standard deviation of 0.3. What percentage of boxes have at least 1 pound of detergent in them?
10. ( Mathisfun.com
) The ages of the population of a town are normally distributed with mean 43 and standard deviation 14 The town has a population of 5,000. How many would you expect to be aged between 22 and 57?
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