A study finds that the amount of radiation required to send

A study finds that the amount of radiation required to send a brain tumor into remission is normally distributed with mean 50 rads and variance 100. Unfortunately, it is also found that patients get radiation sickness at a radiation level that is normally distributed with mean 75 rads and variance 225.
a. What proportion of patients will need a radiation amount of 60 rads or more in order to send their brain tumor into remission?
b. What amount of radiation will make 10% or less of patients get radiation sickness?
c. If the amount of radiation is set such that 10% or less of patients will get radiation sickness, what fraction of patients will receive sufficient radiation to send their tumors into remission?
d. What proportion of samples of sizes 9 have a mean radiation sickness levels between 75 and 85 rads?

Solution

The amount of radiation that will make 10% or less of patients get radiation sickness is calculated using the normal distribution from the z-score table: This is -213 rad.

Using the normal distribution with z-score from previous part. Answer p = 0.004