Step 1: Write out the Z score formula
[tex]\begin{gathered} Z=\frac{x-\mu}{\sigma} \\ x=\text{score} \\ \mu=\operatorname{mean} \\ \sigma=s\tan dard\text{ deviation} \end{gathered}[/tex]Step 2: Calculate the z scores for the two values ( 75 and 80 )
[tex]\begin{gathered} Z_1\Rightarrow z-\text{score for 75} \\ Z_2\Rightarrow z-\text{score for 80} \end{gathered}[/tex][tex]\begin{gathered} Z_1=\frac{75-90}{5}=-\frac{15}{5}=-3 \\ Z_2=\frac{80-90}{5}=-\frac{10}{5}=-2 \end{gathered}[/tex]The probability that the mean is between 75 and 80 will be
[tex]Pr(-3Thus, the probability will be[tex]\begin{gathered} Pr(-3Hence, the indicated probability P(75
