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 μ = 45 and standard deviation σ = 13. 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.)
Solution :
Given that ,
mean = = 45
standard deviation = = 13
(a)
P(x < 60) = P[(x - ) / < (60 - 45) / 13]
= P(z < 1.15)
= 0.8749
(b)
P(x > 16) = 1 - P(x < 16)
= 1 - P[(x - ) / < (16 - 45) / 13]
= 1 - P(z < -2.23)
= 0.9871
(c)
P(16 < x < 60) = P(x < 60) - P(x < 16) = 0.8749 - 0.0129 = 0.862
(d)
P(x > 60) = 1 - P(x < 60)
= 1 - P[(x - ) / < (60 - 45) / 13]
= 1 - P(z < 1.15)
= 0.1251
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