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. 16 0. 4 2. 5 6. 25.

Answer 1

A Z-score or the standard score shows that how many standard deviation for a given measurement deviates from the mean. Total number of standard deviation is 2.5 from the mean 25.

Given information-

The value of the mean of the data is 15.

The value of the standard deviation of the data is 4.

The value of the sample mean is 25.

Normal distribution-

A function that represent the distribution of n numbers of random variables in a symmetrical bell shaped.

Z score-

A Z-score or the standard score shows that how many standard deviation for a given measurement deviates from the mean. The z score for the normal distribution of the data set can be given as,

$Z=\dfrac{X-\mu}{\sigma}$

Here $X$ is the sample mean of the data set, $\mu$ is the population mean of the data set and $\sigma$ is the standard deviation.

Put the values,

$Z=\dfrac{25-15}{4} \\Z=2.5$

Hence, total number of standard deviation is 2.5 from the mean 25.

Learn more about the Z score here;

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