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Question

suppose that IQ scores are approximately normally distributed with a mean of 100 and standard deviation of 10. what percentage of people have IQ scores greater than 125?

Answer 1

Hi Juliana,

 

The first thing we need to do is determine the z-score.

 

        x-μ

z = ------

         σ

 

where x = 125, μ = 100 and σ = 10

 

      125-100        25

z = ----------  = ------ = 2.5

          10             10

 

If we look up 2.5 in a z-table, we get, 0.9938.

 

But recall the values in a z-table represent the area under the normal curve from that point to the left, or less than.

We want the percent of people who have IQ scores greater than 125.

 

1-0.9938 = probability IQ scores are greater than 125.

 

= 0.0062

= 0.62%