advertisement

Math 141 Final Review -Normal Distribution & Probability Name:______________________ The Normal Distribution In a normal distribution: About 68% of the data is within 1 standard deviation of the mean About 95% of the data is within 2 standard deviations of the mean 1)Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test). Draw a graph for a and b. a) Find the probability that a randomly selected adult has an IQ greater than 120. Let x = IQ score convert 120 to a z-score so that you can use the table to find the area under the curve. Remember that AREA = PROBABILITY Z = (120 – 100)/15 = 1.33 P(x > 120) = P(z >1.33) = .5 - .408 = .092 (use the table on pg 754) Note: table shows area from zero to 1.33 . b) Assume that adults have IQ scores that are normally distributed with = 100 and = 15. Find P90, which is the IQ score separating the bottom 90% from the top 10%. Draw the bell curve. Shade 10% area on the right. Draw a vertical line at the starting point of the area. So between z = 0 and that starting point is an area of .40. Find the z-score that corresponds to an area of 0.400. That z-score is 1.28. 1.28 = (x – 100)/15 Solve for x. Answer: x = 119.2 IQ points About 90% of IQ scores are less than 119.2 points. 2)Assume heights of men are normally distributed with mean 69” and Standard deviation 3”. A man is 75” tall. Let x = height. Draw the bell curve. a) What percentage of men are taller than him. In other words, if I randomly select a man, what is the probability that he will be taller than 75”? Z score: z = 75” – 69” = 2 3” P(X > 75”) = P(Z > 2) = .5 - .477 = .023 Look up z = 2 (table) b) What percentage of men are shorter than 69”? 50% c) What percentage of men are shorter than 5 ft? P(x < 60”) = P(z < -3.00) = .5 - .499 = .001 Note that the table only gives areas to the right of z = 0. Use the idea of symmetry. d) What height separates the tallest 25% of men from the shortest 75% of men. To find x we first need to find z. So draw the bell curve and shade an area of 25% on the right. So from z=0 to that cut point is 25%. Look up the zscore that corresponds to an area of 25% (z = .67). Now use the zscore formula to find x. .67 = x – 69” x = 71.01” About 25% of men are taller than 71” 3” Probability: 3) Randomly select two cards. Find the probability of selecting 2 Kings. P(K and K) = (4/52) (3/51) =