what is the probability of a rating of150 and 200 with a deviation of15
To calculate the probability of a rating falling within a specific range, we need to use the concept of the normal distribution. In this case, we'll use the Z-score formula to calculate the probability.
The Z-score formula is given by:
Z = (X - μ) / σ
Where:
Z is the Z-score,
X is the rating value,
μ is the mean (or average) rating,
σ is the standard deviation.
In our case, the mean rating is 150 and the standard deviation is 15.
For a rating of 150:
Z1 = (150 - 150) / 15
Z1 = 0
For a rating of 200:
Z2 = (200 - 150) / 15
Z2 = 3.33
Now, we can use a Z-table or a calculator to find the probability associated with the Z-scores.
Looking up the Z-score of 0 in the Z-table gives us a probability of 0.5, meaning there is a 50% probability of obtaining a rating of 150 or lower.
To find the probability associated with Z2 = 3.33, you would need to refer to the Z-table or use a calculator with a normal distribution function. In this case, the probability will be very small since the Z-score is quite large.
Keep in mind that this probability represents the likelihood of observing a rating within the specific ranges you mentioned, assuming a normal distribution.