Math 141 Final Review -Normal Distribution & Probability
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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) =