a certain standardized tests math scores have a bell - shaped distribution with a mean of 526 and a standard…

Explanation:

Step1: Calculate z - scores

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $x$ is the data - point. Given $\mu = 526$ and $\sigma=115$. For $x = 401$, $z_1=\frac{401 - 526}{115}=\frac{- 125}{115}\approx - 1.09$. For $x = 651$, $z_2=\frac{651 - 526}{115}=\frac{125}{115}\approx1.09$.

Step2: Use the standard normal distribution table

The standard normal distribution table gives the cumulative probability $P(Z < z)$. Looking up $z_1=-1.09$ and $z_2 = 1.09$ in the standard - normal table, we find that $P(Z < - 1.09)=0.1379$ and $P(Z < 1.09)=0.8621$. The probability $P(-1.09<Z<1.09)=P(Z < 1.09)-P(Z < - 1.09)$. $P(-1.09<Z<1.09)=0.8621 - 0.1379=0.7242$.

Step3: Convert to percentage

To convert the probability to a percentage, we multiply by 100. So the percentage of scores between 401 and 651 is $0.7242\times100 = 72.42%\approx72.4%$.

Answer:

72.4%