Question

The mean of a set of normally distributed data is 550 and the standard deviation is 35, If there are 200 values, in the set of data, how many would be between 480 and 620?

Answer 1

It is necessary to apply a correction for continuity to enable the techniques for a continuous Normal distribution to be used to solve this question.
Applying the continuity correction of 0.5, we need to find the z-scores for 480.5 and 619.5.
\[z=\frac{X-\mu}{\sigma}\]
The z-score for 480.5 is
\[z _{1}=\frac{480.5-550}{35}=-1.9857\]
and the z-score for 619.5 is
\[z _{2}=\frac{619.5-550}{35}=1.9857\]
Reference to a standard normal distribution table gives the cumulative probability applying to these two z-scores. Subtracting the smaller cumulative probability from the larger gives the probability of 0.95. Therefore 95% of the set of data lies between 480 and 620.
Now you need to find 95% of 200.