Question

ASSUME THAT ADULTS HAVE IQ SCORES THAT ARE NORMALLY DISTRIBUTED WITH A MEAN OF

105 AND A STANDARD DEVIATION 15.
A. FIND THE PROBABILTY THAT A RANDOMLY selected adult has an iq less than 126

Answer 1

P( A randomly selected adult has an IQ less than 126) = 0.91924

Explanation:

Let, X be the random variable, IQ of an adult.

According to the question,

X
`\sim` Normal (105,15)

Let, Z =
`\frac {X - 105}{15}`

So, Z
`\sim` Normal(0,1)

Now,

X < 126

⇒
`\frac {X - 105}{15}` <
`\frac {21}{15}`

⇒Z < 1.4

Now, from standard normal probability table we get

P(Z < 1.4) = 0.91924

So, P( A randomly selected adult has an IQ less than 126) = 0.91924