assume that adults have iq scores that are normally distributed with a mean of μ = 105 and a standard…

assume that adults have iq scores that are normally distributed with a mean of μ = 105 and a standard deviation σ = 20. find the probability that a randomly selected adult has an iq between 88 and 122. click to view page 1 of the table. click to view page 2 of the table. the probability that a randomly selected adult has an iq between 88 and 122 is (type an integer or decimal rounded to four decimal places as needed.)

assume that adults have iq scores that are normally distributed with a mean of μ = 105 and a standard deviation σ = 20. find the probability that a randomly selected adult has an iq between 88 and 122. click to view page 1 of the table. click to view page 2 of the table. the probability that a randomly selected adult has an iq between 88 and 122 is (type an integer or decimal rounded to four decimal places as needed.)

Answer

Explanation:

Step1: Calculate z - scores

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$. For $x = 88$, $z_1=\frac{88 - 105}{20}=\frac{- 17}{20}=-0.85$. For $x = 122$, $z_2=\frac{122 - 105}{20}=\frac{17}{20}=0.85$.

Step2: Find probabilities from z - table

We know that $P(-0.85<Z<0.85)=P(Z < 0.85)-P(Z<-0.85)$. From the standard normal distribution table, $P(Z < 0.85)=0.8023$ and $P(Z<-0.85)=0.1977$.

Step3: Calculate the final probability

$P(-0.85 < Z < 0.85)=0.8023-0.1977 = 0.6046$.

Answer:

$0.6046$