the scores on a test are normally distributed with a mean of 60 and a standard deviation of 12. what is the…
the scores on a test are normally distributed with a mean of 60 and a standard deviation of 12. what is the score that is $2\frac{1}{2}$ standard deviations above the mean?\na score of is $2\frac{1}{2}$ standard deviations above the mean.
Answer
Explanation:
Step1: Identify the formula
The formula to find a value (x) in a normal - distribution given the mean (\mu), standard deviation (\sigma), and the number of standard deviations (z) is (x=\mu + z\sigma).
Step2: Substitute the given values
We are given that (\mu = 60), (\sigma=12), and (z = 2.5). Substitute these values into the formula: (x=60+2.5\times12).
Step3: Calculate the result
First, calculate (2.5\times12 = 30). Then, (x=60 + 30=90).
Answer:
90