Question

The annual assets for First Michigan corporation is approximately normally distributed with standard deviation 20 million. The mean is not known. However it is known that 57% of the assets is over 217.5 million. Find the mean assets value in millions. Answer to 2 decimal places.

Answer 1

Solution:-

Given that,

= 21.5

standard deviation = = 20

Using standard normal table,

P(Z > z) = 57%

= 1 - P(Z < z) = 0.57  

= P(Z < z) = 1 - 0.57

= P(Z < z ) = 0.43

= P(Z <-0.18 ) = 0.43

z =-0.18

Using z-score formula,

x = z * +

x = -0.18* 20+21.5

x = 17.9