Given that IQ scores are normally distributed with a mean of 100 and a standard deviation of 15

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 Quiz

Find the indicated value:

1.  z.05    = ___-1.645____ (2 pts)

2.  Given that IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, find the probability of randomly selecting someone with an IQ between 100 and 120. (5 pts)

Z = 120-100 /15 = 1.33

Look up z = 1.33 in the z-table à 0.9082

 

100-.9082= 9.18      9.18% or 90.82%

There is a 9.18% probability that randomly selecting someone with an IQ between 100 and 120

 

3.  Given that IQ scores are normally distributed with a mean of 100 and standard deviation of 15, find the number of IQ points that separate the bottom 25% and the top 25%.  (5 pts)

 4. M&M plain candies have a normally distributed weight with a mean of 0.8565 g and a standard deviation of 0.0518 g.  If 465 M&M plain candies are randomly selected, find the probability that their mean weight is at least 0.8535 g each. (5 pts)

5. Assume that 75% of the U.S. driving population have been ticketed for at least one speeding violation.  If you choose 200 people to sample, what is the probability that less than 80% of these people have a speeding ticket on their driving record?    (5 pts)

n = 200  p= .75  q =. 15  p̂ = .80 

σ p̂ = 75.15/ 200 0.023717 

z = 80-75 / 0.023717 = 2.108192 

z table à 0.982484505283742 

1-0.982484505283742 = 0.0175 

1.75% chance that less than 80% of these people have a speeding ticket on their driving record

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