Question

Data with 760 observations are drawn from a bell-shaped distribution with a mean of 66 and a standard deviation of 16. Approximately how many observations are more than 98?

What is the number of observations?

Answer 1

We have 760 observations, so N = 760

mean is 66 and standard deviation is 16

we know that in a bell shaped distribution, only 2.3% of data values lies above 2 standard deviation from the mean.

This means that only 2.3% of data values fall in the region(greater than 2 standard deviation from the mean)

Using the data, we can see that mean + 2(standard deviation) = 66 + 2(16) = 66+32 = 98

So, 98 is exactly at a point which is 2 standard deviation above the mean.

So, 2.3% of the data values out of all 760 observations are more than 98

2.3% of 760 = (2.3/100)*760 = 0.023*760 = 17.48...................rounding it to next whole number, we get 18

So, we can say that 18 observations are above 98