Question

1)  Average tire life is 30,000 miles (μ = 30,000) and σ = 2,300 miles.  What is the

     probability that a tire will last 35,000 miles (or more)?

2)  If μ = 130 and σ = 20 on an employment test and the company only hires from the top

     75% of scores, what is the lowest score you can get and still get hired?

3)  The SAT has μ = 500 and σ = 100.  What score would put you in the top 15%?

4)  For a standard IQ test, μ = 100 and σ = 15.  

      a) What IQ would put you in the top 10%?

      b) If your IQ was 135, what percentage of the population is smarter than you?

Answer 1

1)

μ = 30,000

σ = 2,300

P( X> 35000) = P ( (X - μ) /σ > (35000-30000) / 2300 ) = P ( Z > 2.17) = 1- P(Z <2.17) = 1- (2.17) = 1- .985 = 0.015

2)

μ = 130

σ = 20

P(Z> Z') =0.75

or, P( Z <Z') = 0.25

or, Z' = -.675 [ From standard normal table, since (-0.675) = 0.25

or, (X - μ) /σ = - 0.675

or, X= 116.5

The lowest score I can get and still get hired is 116.5

3)

μ = 500

σ = 100

P(Z> Z') =0.15

or, P( Z <Z') = 1.04

or, Z' = -.675 [ From standard normal table, since (1.04) = 0.85

or, (X - μ) /σ = 1.04

or, X= 604

If my score is greater than 604, I would be in top 15 %.

4)

a)

μ = 100

σ = 15

P(Z> Z') =0.10

or, P( Z <Z') = 1.28

or, Z' = -.675 [ From standard normal table, since (1.28) = 0.90

or, (X - μ) /σ = 1.28

or, X= 119.2

If my IQ is greater than 119.2, I would be in top 10 %.

b)

P(X > 135)

=P( (X - μ) /σ > (135 - 100 ) /15 ) = P( Z > 2.33) = 1- 0.99010 = 0.0099

So, 0.99 %  of the population is smarter than me.

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