scores on a national math test are normally distributed, with a mean score of 490 and a standard deviation…

scores on a national math test are normally distributed, with a mean score of 490 and a standard deviation of 50. which test score represents the top 20%, rounded to the nearest whole number? find the z - table here. 426 448 532 554
Answer
Answer:
C. 532
Explanation:
Step1: Find the z - score
We want the top 20%, so the area to the left is $1 - 0.20=0.80$. Looking up in the z - table, the z - score corresponding to an area of 0.80 is approximately $z = 0.84$.
Step2: Use the z - score formula
The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value we want to find, $\mu$ is the mean, and $\sigma$ is the standard deviation. We know $\mu = 490$, $\sigma = 50$, and $z = 0.84$. Rearranging the formula for $x$ gives $x=\mu+z\sigma$.
Step3: Calculate the test score
Substitute the values into the formula: $x = 490+0.84\times50=490 + 42=532$.