Question

In a distribution where the mean is 80 and the standard deviation is 5​, find the largest fraction of the numbers that could meet the following requirements. less than 70 or more than 90

Answer 1

Solution :

Given that,

mean = = 80

standard deviation = = 5

P( x < 70 )

P ( x - / ) < ( 70 - 80 / 5)

P ( z < -10 / 5 )

P ( z < - 2 )

= 0.0228

P (x > 90 )

= 1 - P (x < 90 )

= 1 - P ( x -  / ) < (90 - 80 / 5)

= 1 - P ( z < 10 / 5 )

= 1 - P ( z < 2 )

Using z table

= 1 - 0.9772

= 0.0228

= 0.0228 + 0.0228

Probability = 0.0456