Respuesta :
Answer:
25 is 2.5 standard deviations from the mean.
Step-by-step explanation:
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean.
In this question:
Mean of 15 and a standard deviation of 4, so [tex]\mu = 15, \sigma = 4[/tex]
How many standard deviations from the mean is 25?
We have to find Z when [tex]X = 25[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{25 - 15}{4}[/tex]
[tex]Z = 2.5[/tex]
So 25 is 2.5 standard deviations from the mean.
