Question

A particular type of 4th grade Achievement Test provides overall scores that are normally distributed with a mean of 50 and a standard deviation of 10.
What is the probability that a randomly selected student earns a score between 33 and 48?

Answer 1

Answer:

The probability that a randomly selected student earns a score between 33 and 48 is 0.3761

Step-by-step explanation:

We compute the z-score related to some value x as $z=\frac{x-50}{10}$. The z-score related to 33 is given by $z_{1}=\frac{33-50}{10}=-1.7$ and the z-score related to 48 is given by $z_{2}=\frac{48-50}{10}=-0.2$. Therefore, the probability that a randomly selected student earns a score between 33 and 48 is given by P(-1.7 < Z < -0.2) = P(Z < -0.2) - P(Z < -1.7) = 0.4207 - 0.0446 = 0.3761.