Respuesta :
ANSWER
[tex]\begin{equation*} 0.40824 \end{equation*}[/tex]EXPLANATION
We want to find the probability that a randomly selected adult has an IQ between 100 and 120.
To do this, first, we have to find the z-score for 100 and 120 using the formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where x = IQ score
σ = standard deviation
μ = mean
Hence, for an IQ score of 100, the z-score is:
[tex]\begin{gathered} z=\frac{100-100}{15}=\frac{0}{15} \\ z=0 \end{gathered}[/tex]For an IQ score of 120, the z-score is:
[tex]\begin{gathered} z=\frac{120-100}{15}=\frac{20}{15} \\ z=1.33 \end{gathered}[/tex]Now, to find the probability of an IQ score between 100 and 120, apply the formula:
[tex]\begin{gathered} P(100Using the standard normal table, we have that:[tex]\begin{gathered} P(z<1.33)=0.90824 \\ P(z<0)=0.5 \end{gathered}[/tex]Therefore, the probability is:
[tex]\begin{gathered} P(0That is the answer.