: 150 scores on a test are normally distributed with a mean of 92 and a standards deviation of 11.5
1) Find z score corresponding to a score of 69. Show work.
To find the z-score corresponding to a score of 69 in a normally distributed population, you can use the formula:
z = (x - μ) / σ
where:
- z is the z-score
- x is the value you want to convert to a z-score (in this case, 69)
- μ is the mean of the distribution (92)
- σ is the standard deviation of the distribution (11.5)
Now, let's substitute the values into the formula:
z = (69 - 92) / 11.5
z = -23 / 11.5
z = -2
Therefore, the z-score corresponding to a score of 69 is -2.