IQ scores are designed to have a mean of 100 and a standard

IQ scores are designed to have a mean of 100 and a standard deviation of 15. IQ testing is one way on which people are categorized as having different levels of metal disability; there are four levels of mental retardation between the IQ scores of 0 and 70.

A.Must show your work: People with Iq scores of 20-35 are said to have severe mental retardation and can learn only basic skills. What percentage of people fall into this range? FYI, it can\'t be 100%.

Solution

Here we have given that, IQ scores which has a mean 100 and standard deviation is 15.

IQ testing is one way on which people are categorized as having different levels of metal disability; there are four levels of mental retardation between the IQ scores of 0 and 70.

We have to calculate percentage of IQ scores of 20-35 are said to have severe mental retardation and can learn only basic skills.

This means we have to calculate here probability first and then percentage.

Let X be a random variable as IQ-score of people.

P( 20 < X < 35)

We can calculate this probability by using z-score.

z-score = (X - µ) /

where µ is mean of the distribution.

and is standard deviation of the distribution.

First we calculate z-score for x=20,

z-score = (20-100) / 15 = -5.33

Again we find z-score for x=35,

z-score = (35-100) / 15 = -4.33

That is we have to find the P(-5.33 < Z < -4.33)

P(-5.33 < Z < -4.33) = P(Z < -4.33) - P(Z < -5.33)

But in the statistical table the available probabilities are upto -3.4 after -3.4 the probability will near by 0.

Since -4.33 and -5.33 are less than -3.4 thats why both the probabilities P(Z < -4.33) and P(Z < -5.33) are 0 so

P(-5.33 < Z < -4.33) = 0

Therefore the required percentage of people fall into 20-35 range = 0*100% = 0%

Hence the answer.