Suppose ages of people who own their homes are normally distributed with a mean of 42 years and a standard deviation of 3.2 years. Approximately 75% of the home owners are older than what age?

38.2

39.9

44.2

48.6

The scores for a bowling tournament are normally distributed with a mean of 240 and a standard deviation of 100. Julian scored 240 at the tournament. What percent of bowlers scored less than Julian?

10%

25%

50%

75%

The odometer readings on a random sample of identical model sports cars are normally distributed with a mean of 120,000 miles and a standard deviation of 30,000 miles. Consider a group of 6000 sports cars. Approximately how many sports cars will have less than 150,000 miles on the odometer?

300

951

5048

5700

Let the required number of home owners be x, then P(z > (x - 42)/3.2) = 0.75
1 - P(z < (x - 42)/3.2) = 0.75
P(z < (x - 42)/3.2) = 0.25
P(z < (x - 42)/3.2) = P(z < -0.6745)
(x - 42)/3.2 = -0.6745
x - 42 = -2.1584
x = -2.1584 + 42 = 39.84 ≈ 39.9

P(z < (240 - 240)/100) = P(z < 0) = 0.5
Required percentage = 50%

P(z < (150,000 - 120,000)/30,000) = P(z < 1) = 0.84134
Required number of cars = 0.84134 x 6,000 = 5,048

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