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

Answer:

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

Step-by-step 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