Answer :
The GRE Scores are represented as ~N(310,12)
In order to find the proportion of scores between 286 and 322, we need to standardize the scores so we can use the standard normal probabilities. Thus, we will find the z-score.
[tex]z-score = \frac{286 - 310}{12} = -2[/tex]
[tex]z-score = \frac{322 - 310}{12} = 1 [/tex]
By looking on the standard normal probabilities table, we find the proportion of scores less than -2.
P(z < -2) = 0.0228
Then, we find the proportion of scores less than 1.
P(z < 1) = 0.8413
To find the proportion between -2 and 1, we subtract the two.
P(-2 < z < 1) = 0.8413 - 0.0228 = 0.8185 = 81.85%
Therefore, 82% of scores are between 286 and 322
In order to find the proportion of scores between 286 and 322, we need to standardize the scores so we can use the standard normal probabilities. Thus, we will find the z-score.
[tex]z-score = \frac{286 - 310}{12} = -2[/tex]
[tex]z-score = \frac{322 - 310}{12} = 1 [/tex]
By looking on the standard normal probabilities table, we find the proportion of scores less than -2.
P(z < -2) = 0.0228
Then, we find the proportion of scores less than 1.
P(z < 1) = 0.8413
To find the proportion between -2 and 1, we subtract the two.
P(-2 < z < 1) = 0.8413 - 0.0228 = 0.8185 = 81.85%
Therefore, 82% of scores are between 286 and 322
Answer:82% of scores are between 286 and 322
Step-by-step explanation:
