Question

Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let x be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy circles, x is approximately normally distributed with mean - 45 and standard deviation - 11. Find the following probabilities. (Round your answers to four decimal places.) (a) x is less than 60 (b) x is greater than 16 (c) x is between 16 and 60 (d) x is more than 60 (This may indicate an infection, anemia, or another type of illness.)

Answer 1

According to the question, ANN(45,112) . &Z= X-M ~ N(0,1) + z = -25 NNI OD (a) P(x660) =PL44560" = P/ ZC 1.36 - $(1-36) -9.9184 (From table of Standard Normal = 0.2131 distribution) (6) P(X> 16) = P(z) 16-45 = P(Z >=264) = P(Z <2.64 = 0(2164) - 0.9958

(0 p(166x660) 60-451 -pocks (265.0-609 = P(-264 < ZL 136) = 0 (136) - 0(-2-66 = 0.9131-0.00915 - 0.90895 (d) P(x>60) =P(z) 60-45) = Plz) 1-36) = |- (1-36) -|- 0.9131 - 0.0869
The area values are calculated using standard normal distribution table.