iq scores are normally distributed with a mean of 100 and a standard deviation of 15. what is the…

Explanation:

Step1: Calculate z - scores

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $x$ is the value from the data set. For $x = 62$, $z_1=\frac{62 - 100}{15}=\frac{- 38}{15}\approx - 2.53$. For $x = 106$, $z_2=\frac{106 - 100}{15}=\frac{6}{15}=0.4$.

Step2: Use the standard normal distribution table

We want to find $P(-2.53<Z<0.4)$. We know that $P(-2.53<Z<0.4)=P(Z < 0.4)-P(Z < - 2.53)$. From the standard - normal distribution table, $P(Z < 0.4)=0.6554$ and $P(Z < - 2.53)=0.0057$.

Step3: Calculate the probability

$P(-2.53<Z<0.4)=0.6554 - 0.0057=0.6497\approx0.650$.

Answer:

$0.650$