Question

Using excel and the functions

IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X = IQ of an individual.

1. X ~ _____(_____,_____)
2. Find the probability that the person has an IQ greater than 120. Include a sketch of the graph, and write a probability statement.
3. MENSA is an organization whose members have the top 2% of all IQs. Find the minimum IQ needed to qualify for the MENSA organization. Sketch the graph, and write the probability statement.
4. The middle 50% of IQs fall between what two values? Sketch the graph and write the probability statement.

Answer 1

Here

Here we need to find

As distribution is normal we can convert x to z

Here we need to find x such that

Using z table we get

So

Hence

Now we need to find x1 and x2 such that

Using z table we get

So

And