A normal distribution of data has a mean of 15 and a standard deviation of 4. How many standard deviations from the mean is 252

0 0.16

0.4

0 2.5

O 6.25

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A normal distribution of data has a mean of 15 and a standard deviation of 4. How many standard deviations from the mean is 252

0 0.16

0.4

0 2.5

O 6.25

Third option is correct.

Step-by-step explanation:

Since we have given that

Mean [tex](\mu)=15[/tex]

Standard deviation [tex]\sigma=4[/tex]

Mean (X) = 25

We need to find the "Number of standard deviations (Z) from the mean (X) ":

As we know that in Normal distribution:

[tex]Z=\frac{X-\mu}{\sigma}\\\\Z=\frac{25-15}{4}\\\\Z=\frac{10}{4}\\\\Z=2.5[/tex]

Hence, Third option is correct.

This is the concept of probability, to get the number of standard deviations that 25 is from the mean, we calculate the z-score given by:

Z=(X-mean)/s.d

where;

x=25

mean=15

s.d=4

hence;

z=(25-15)/4=2.5

The answer is 2.5

So the difference from the mean and the value is:

25 - 15 = 10

and now we need to know how many standard deviations of 4 are in that range, that is:

10/4 = 2.5

so there are 2.5 std deviations from the mean if the value is 25

2.5 standard deviations

Step-by-step explanation:

The difference from the mean and the value is:

25 - 15 = 10

how many standard deviations of 4 are in that range:

10/4 = 2.5

There are 2.5 std deviations from the mean if the value is 25

Z=[tex]\frac{25-15}{4}[/tex]=2.5 This is in standardized units, or z-score.

What were your given answer choices