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 μ = 40 and standard deviation σ = 15. Find the following probabilities. (Round your answers to four decimal places.)

(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

• a)

  Here, μ = 40, σ = 15 and x = 16. We need to compute P(X >= 16). The corresponding z-value is calculated using Central Limit Theorem

  z = (x - μ)/σ
  z = (16 - 40)/15 = -1.6

  Therefore,
  P(X >= 16) = P(z <= (16 - 40)/15)
  = P(z >= -1.6)
  = 1 - 0.0548 = 0.9452

  
  b)

  Here, μ = 40, σ = 15, x1 = 16 and x2 = 60. We need to compute P(16<= X <= 60). The corresponding z-value is calculated using Central Limit Theorem

  z = (x - μ)/σ
  z1 = (16 - 40)/15 = -1.6
  z2 = (60 - 40)/15 = 1.33

  Therefore, we get
  P(16 <= X <= 60) = P((60 - 40)/15) <= z <= (60 - 40)/15)
  = P(-1.6 <= z <= 1.33) = P(z <= 1.33) - P(z <= -1.6)
  = 0.9082 - 0.0548
  = 0.8534

  
  c)

  Here, μ = 40, σ = 15 and x = 60. We need to compute P(X >= 60). The corresponding z-value is calculated using Central Limit Theorem

  z = (x - μ)/σ
  z = (60 - 40)/15 = 1.33

  Therefore,
  P(X >= 60) = P(z <= (60 - 40)/15)
  = P(z >= 1.33)
  = 1 - 0.9082 = 0.0918