Question

a normal distribution of data has a mean of 15 and a standard deviation of 4. how many standard deviations from the mean is 25?
0.25
0.4
2.5
6.25

Explanation:

Step1: Recall the z-score formula

The z - score formula is \( z=\frac{x - \mu}{\sigma} \), where \( x \) is the value from the data set, \( \mu \) is the mean, and \( \sigma \) is the standard deviation. The z - score tells us how many standard deviations a value \( x \) is from the mean.

Step2: Identify the values

We are given that \( \mu = 15 \), \( \sigma=4 \), and \( x = 25 \).

Step3: Substitute the values into the formula

Substitute \( x = 25 \), \( \mu=15 \), and \( \sigma = 4 \) into the z - score formula:
\( z=\frac{25 - 15}{4}=\frac{10}{4}=2.5 \)

Answer:

2.5 (corresponding to the option with 2.5)