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  1. Use technology or a z-distribution table to find the indicated area. The expression P(z<2.87)P(z<2.87) represents the area under the standard normal curve below a given value of z. What is P(z<2.87)P(z<2.87)?
A0.0027
B0.0021
C0.9973
D0.9979

  1. Use technology or a z-distribution table to find the indicated area. 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?
A10%
B25%
C50%
D75%

  1. Use technology or a z-distribution table to find the indicated area. 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?
A300
B951
C5048
D5700

  1. The number 0.6064 represents the area under the standard normal curve below a particular z-score. What is the z-score? Enter your answer, as a decimal to the nearest hundredth, in the box.

  2. Use technology or a z-distribution table to find the indicated area. 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?
A38.2
B39.9
C44.2
D48.6

Verified Answer :

nobillionaireNobley

1.) P(z < 2.87) = 0.9979

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

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

4.) Required z-score = 0.27

5.) 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

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