how do i find the answer

Question

An IQ test has a mean of 100 and a standard deviation of 15. The test scores are normally distributed. Find the percentage of people who will score below 93. Give your answer as a percent rounded to two decimal places (to the nearest hundredth).

Answer 1

You would want to find a Z table that computes area under the curve to the left of a given z score.

 

Then, compute the Z score for 93 using z = (x - μ)/σ = (93 - 100)/15 = -7/15 = .4667

 

By symmetry, the area to the left of -0.4667 is equal to the area to the right of +0.4667

 

We can then take the entire area under the normal curve (which is 1) and subtract the area to the left of +0.4667 and that will give us a value equal to the area to the left of z = -0.4667

 

P( x < 93) = P( z < -0.4667) = 1 - P( z > +0.4667) = 1 - 0.6808 (which is from the table) = .3192

 

Approximately 31.92% of the people are below an IQ of 93.

 

Alternatively, you can use a graphing calculator to do the calculation for you.

 

On a TI-83 or 84, you can go to DISTR and select normalcdf( lower bound, upper bound, mean, std dev)

 

in this case normalcdf( 0, 93, 100, 15) would give you the same answer as the work above.

Answer 2

 

µ = 100

 

Standard deviation= 15

 

Z= (93 - 100)/15

 

-7/15 = -.4666

 

0.5 - .4666 = 0.0334

 

3.34%