Question

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

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