Question

practice problem: what rule do we use? lets work through a problem where youll need to determine the correct rule based on the information provided. youll complete all four steps to find the final answer. if a score is selected at random from a normal distribution with: $mu = 100$ and $sigma = 20$, what is the exact probability that the score will be 110 or less? steps to solve this problem: 1. choose the correct rule based on the wording of the question 2. compute the z - score, then draw and shade the normal distribution 3. look up the proportion below z using the z - table 4. report the final probability as your answer now, select the correct interpretation (step 4) from the answer choices below. the exact probability of drawing a score of 110 or more from a normal distribution with $mu = 100$ and $sigma = 20$ is $p = .3085$. the exact probability of drawing a score of 110 or less from a normal distribution with $mu = 100$ and $sigma = 20$ is $p = .6915$. the exact probability of drawing a score of 110 or less from a normal distribution with $mu = 100$ and $sigma = 20$ is $p = .3830$. the exact probability of drawing a score of 110 or less from a normal distribution with $mu = 100$ and $sigma = 20$ is $p = .3085$.

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 110$, $\mu=100$, and $\sigma = 20$. So, $z=\frac{110 - 100}{20}=\frac{10}{20}=0.5$.

Step2: Use the z - table

We look up the value of $z = 0.5$ in the standard normal distribution (z - table). The value corresponding to $z = 0.5$ in the z - table gives the proportion of the area under the curve to the left of $z$. Looking up $z=0.5$ in the z - table, we find that the value is approximately $0.6915$.

Answer:

The exact probability of drawing a score of 110 or less from a normal distribution with $\mu = 100$ and $\sigma=20$ is $p = 0.6915$. So the correct option is: The exact probability of drawing a score of 110 or less from a normal distribution with $\mu = 100$ and $\sigma = 20$ is $p=0.6915$.