in a distribution of scores with a mean of 1500 and a standard deviation of 250, what is the 95th percentile?

To find the 95th percentile in a distribution of scores with a mean and standard deviation, we can use the concept of the standard normal distribution.

Step 1: Standardize the value
The first step is to standardize the desired percentile value by subtracting the mean (1500) from it and dividing the result by the standard deviation (250).

Standardized value = (desired percentile - mean) / standard deviation
Standardized value = (95 - 1500) / 250
Standardized value = -1.4

Step 2: Lookup the value in the standard normal distribution table
Next, we need to consult a standard normal distribution table (also known as a Z-table) to find the corresponding value for the standardized value we calculated in Step 1. The table provides the percentage of values that fall below a given standardized value.

Looking up the standardized value -1.4 in the table, we find that it corresponds to a cumulative probability of approximately 0.0808.

Step 3: Calculate the percentile value
To find the actual percentile value, we subtract the cumulative probability from 1 and multiply the result by 100.

Percentile value = (1 - cumulative probability) * 100
Percentile value = (1 - 0.0808) * 100
Percentile value = 91.92 (rounded to two decimal places)

Therefore, the 95th percentile in the distribution of scores with a mean of 1500 and a standard deviation of 250 is approximately 91.92.

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion and its Z score.

Z = (score-mean)/SD

Insert the values to find the score.