Question

A symmetric, bell-shaped data set has a mean of 25, a standard deviation of 1.7 and a sample size of 500. Find the following: (Round appropriately)

   a.) The number of data points less than 22: ____________

  

   b.) The number of data points between 23 and 27: ____________

   c.) The number of data points greater than 28: ____________

Answer 1

Here we have n = 500, = 25, = 1.7

x ~ N ( )

a) The number of data points less than 22:

p ( x < 22 )

= p ( z < -1.76 )

= 0.0392 ----------- looking in to standard normal probability table acoss z value -1.7 and 0.06

b) The number of data points between 23 and 27:

p ( 23 < x < 27 )

= p ( -1.17 < z < 1.17 )

= p ( Z < 1.17 ) - p ( z < - 1.17 )

= 0.8790 - 0.121

= 0.758

c) The number of data points greater than 28:

p ( x > 28 )

= p ( z > 1.76 )

= 1 - p ( z 1.76 )

= 1 - 0.9608

= 0.0392