scores on a test are normally distributed with a mean of 81 and a standard deviation of 8. Find the probability that a randomly chosen score will be between 70 and 93.

Answer:0.8486Explanation:To find the probability that a score will be between 70 and 93, we first need to standardize these values, so we will use the following[tex]z=\frac{value-mean}{standard\text{ deviation}}[/tex]Therefore, for 70 and 93, we get[tex]\begin{gathered} z=\frac{70-81}{8}=-1.375 \\ \\ z=\frac{93-81}{8}=1.5 \end{gathered}[/tex]Then, we need to find the following probabilityP(-1.375 < z < 1.5)This probability can be calculate using a standard normal table, soP(-1.375 < z < 1.5) = P(z < 1.5) - P(z < -1.375)P(-1.375 < z < 1.5) = 0.9332 - 0.0846P(-1.375 < z < 1.5) = 0.8486Therefore, the probability is 0.8486