Question

Assume that adults have IQ scores that are normally distributed with a mean of mu equals 105 and a standard deviation sigma equals 15. Find the probability that a randomly selected adult has an IQ between 90 and 120.

Answer 1

Answer:   0.6827

Step-by-step explanation:

Given : Mean IQ score : $\mu=105$

Standard deviation : $\sigma=15$

We assume that adults have IQ scores that are normally distributed .

Let x be the random variable that represents the IQ score of adults .

z-score : $z=\dfrac{x-\mu}{\sigma}$

For x= 90

$z=\dfrac{90-105}{15}\approx-1$

For x= 120

$z=\dfrac{120-105}{15}\approx1$

By using the standard normal distribution table , we have

The p-value : $P(90$

$P(z$

Hence,  the probability that a randomly selected adult has an IQ between 90 and 120 =0.6827

Answer 2

Answer:

Step-by-step explanation:

Let X be the IQ scores of adults

Given that X is normally distributed with a mean of mu equals 105 and a standard deviation sigma equals 15.

Thus Z score corresponding to any X would be

$\frac{x-105}{15}$\

Required probability

=probability that a randomly selected adult has an IQ between 90 and 120.

=P(90<X<120)

= P(-1<z<1)

= 0.6836