Question

Suppose a normally distributed set of data with 2100 observations has a mean of 130 and a standard deviation of 19. Use the 68-95-99.7 Rule to determine the number of observations in the data set expected to be above a value of 111. Round your answer to the nearest whole value.

Answer 1

Solution:

Given, X follows Normal distribution with,

   = 130

= 19

Note that 111 = 130 - 19 = -   

P(X > 111) = P[X > - ] = 34 + 34+ 13.5 + 2.35 + 0.15 = 84 %

  number of observations in the data set expected to be above a value of 111

= n * p

= 2100 * 0.84

= 1764