PLEASE HELP ON THIS QUESTION ASAP

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 adults, x is approximately normally distributed with mean 38 and standard deviation 12. what is the probability that

(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.)

please show step by step to each question

Answer 1

a) z = (x-µ)/σ = (60-38)/12 ≈ 1.833; P( z < 1.833 ) ≈ 0.967

b) z = (x-µ)/σ = (16-38)/12 ≈ -1.833; P( z > -1.833 ) ≈ 0.967

c) 0.933; calculate area up to 60 - area less than 16 OR cumulative area under z curve to 1.833 - cumulative area under z curve to -1.833, which z scores were calculated in (a) and (b) above.

d) 1-0.967, from (a) ≈0.033