Project 8: Normal Distribution: Middle Area
A z-score is the number of standard deviations above/below the mean a certain value is.
Suppose IQ score are normally distributed with mean 100 and SD 15
A person who has an IQ of 85 has a z-score of -1.
A person with an IQ of 145 has a z-score of 3.
A person with an IQ of 120 has a z-score of 20/15 = 1.333
normalcdf(lowerZ, upperZ) returns the area (proportion) under the normal curve between z = lower and z = upper.
normalcdf(-1, 0) returns .3413
normalcdf(-1, 1) returns .6826
normalcdf(-1, 2) returns .8185
normalcdf(0, 10) returns .5
normalcdf(-100,0) returns .5
invNorm(leftTailArea) returns the z-score with left tail area given
invNorm(.0227) returns -2
invNorm(.5) returns 0
invNorm(.8412) returns 1
invNorm(.75) returns .6744
Example 1: Adult IQ scores are normally distributed with mean 100 and sd 15. What proportion of adults have an IQ less than 90?
z = (90-100)/15 = -.666
normalcdf(-10, -.666) = .255 so about 25.5% of adults have an IQ score less than 90.
Example 2: Adult IQ scores are normally distributed with mean 100 and sd 15. What IQ score is at the top 10% of IQ scores?
z = invNorm(.9) because 90% of scores are less than this score (left-tail area)
z = 1.28 which means the adult has an IQ score 1.28 standard deviations above the mean
1.28*15 + 100 is about 119 so an adult would need an IQ of about 119 to be at the top 10% of IQ scores.
Project 8: Variables 'mean', 'sd', 'x1', 'x2' have been initialized. Working methods normalcdf and invNorm are available.
Methods normalcdf(lowerZ, upperZ) and invNorm(leftArea) work as shown above.
Task: Appropriately assign the values of 'z1', 'z2', 'middleArea'
z1 represents the z-score for x1 (how many standard deviations above/below the mean x1 is)
z2 represents the z-score for x2 (how many standard deviations above/below the mean x2 is)
middleArea represents the probability of obtaining a value between x1 and x2 from this distribution.
**If your code works for 5 test cases in a row, you can enter your e-mail address.