Question

4. The amount of radiation that can be absorbed by humans before death is normally distributed with a mean of 500 units and a standard deviation of 150. Above what dosage level will only 5% survive?

Answer 1

Solution:-

Given that,

mean = = 500

standard deviation = = 150

Using standard normal table,

P(Z > z) = 5%

= 1 - P(Z < z) = 0.05  

= P(Z < z) = 1 - 0.05

= P(Z < z ) = 0.95

= P(Z < 1.645 ) = 0.95

z = 1.645

Using z-score formula,

x = z * +

x = 1.645 * 150 + 500

x = 746.75 units