Answer :
Step 1:
Write the given data
[tex]\begin{gathered} \text{mean }\mu\text{ = 2524} \\ \text{Standard deviation }\sigma\text{ = 325} \\ x\text{ = 1979} \end{gathered}[/tex]Step 2:
Write the z-score formula
[tex]z\text{ = }\frac{\text{x - }\mu}{\sigma}[/tex]Step 3
Substitute the values in the z score equation
[tex]\begin{gathered} \text{z = }\frac{1979\text{ - 2524}}{325} \\ z\text{ = }\frac{-545}{325} \\ z\text{ = -1.677} \end{gathered}[/tex]Step 4:
Draw the z-curve
Step 5
Probability that scores greater than 1979 id Pr (z > -1.677)
[tex]=\text{ 0.5 - 0.0475 + 0.5 = }0.953[/tex][tex]\begin{gathered} percentageofscoresgreaterthan1979 \\ =\text{ 0.953 }\times\text{ 100 = 95.3\%} \end{gathered}[/tex]Final answer
= 95.4%
