Question

In a given school, 3 out of 10 people tend to have IQ level of more than 150.

1. If a group of 100 people were to be picked from this school, what is the probability of getting 80 people that have IQ below 150.

b. What is the expected number of people with IQ over 150 in a group of 100.

Answer 1

Solution:

In a given school, 3 out of 10 people tend to have IQ level of more than 150.

Probability that IQ level of more than 150 , p = 3/10 = 0.30

and, similarly, the probability that IQ level below 150 = 1 - 0.30 = 0.70

Now,

(a) If a group of 100 people were to be picked from this school, then the probability of getting 80 people that have IQ below 150 is given by,

Sample Size, n = 100

By using Binomial distribution, we have,

The probability of getting 80 people that have IQ below 150 is given by,

   (Round to four decimal places)

Also, we can solve by using EXCEL " BINOMDIST(80,100,0.7,0) ",

(b) The expected number of people with IQ over 150 in a group of 100 is given by,

We know that Expected value = np = 100(0.30) = 30

So, the expected number of people with IQ over 150 in a group of 100 is 30.