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

Question

Mathematics

Zoey Greene

21 September, 23:51

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

+4

Answers (1)

Know the Answer?

Heidi Anderson · Answer 1

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