Answer:
2.4
Step-by-step explanation:
To obtain the z value, subtract the mean (75) from the given value (87) and divide the result by the standard deviation (5). The answer is 2.4.
The standard deviations away from the mean is the recorded value 87 when a mean of 75 and a standard deviation of 5 is 2.4.
Normally distributed data is the distribution of probability which is symmetric about the mean. The mean of the data is the average value of the given data.
The standard deviation of the data is the half of the difference of the highest value and mean of the data set.
Consider a normally distributed data set with a mean μ of 75 and a standard deviation σ of 5.
One of the recorded values X is 87. To find the away value, we have to find the z score using the following formula,
[tex]Z=\dfrac{X-\mu}{\sigma}[/tex]
Here, X is the sample size, μ is the mean and σ is the standard deviation of the data. Put the values,
[tex]Z=\dfrac{87-75}{5}\\Z=2.4[/tex]
Thus, the standard deviations away from the mean is the recorded value 87 when a mean of 75 and a standard deviation of 5 is 2.4.
Learn more about the normally distributed data here;
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