Answer to Question #309505 in Statistics and Probability for Subodh

Question

If the amount of cosmic radiation to which a person is exposed while flying by jet across the United States is a random variable having the normal distribution with mean as

4.35 mrem and standard deviation as 0.59 mrem. Find the probabilities that the amount of cosmic radiation to which a person is exposed on such a flight is: 

a) Between 4.00 mrem to 5.00 mrem, 

b) At least 5.50 mrem, 

c) No more than 4.5 mrem.

Answer 1

we define the following

a) p(4<x<5), given mean =4.35 and standard deviation=0.59, we use z calculations as below

z(4) = (4 - 4.35) / (0.59) = -0.59

z(5) = (5- 4.35) / (0.59) = 1.10

hence p(4<x<5) = p(-0.59 < z <1.10), using normal tables we obtain

(0.86433 - 0.27760) = 0.58673

b) we define p(x≥5.5), using z calculations , we have

z(5.5) = (5.5 - 4.35) / (0.59) = 1.95

hence p(x≥5.5) = 1 - p(z<1.95) = (1 - 0.97441) = 0.02559

c) we define p(x≤4.5), using z calculations, we have

z(4.5) = (4.5 - 4.35) / (0.59) = 0.25

hence p(x≤4.5) = p(z<0.25), using normal tables we have

= 0.59871