Question

3)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 = 14. 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.)

4) Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of 8.4 minutes and a standard deviation of 1.7 minutes. For a randomly received emergency call, find the following probabilities. (Round your answers to four decimal places.)

(a) the response time is between 5 and 10 minutes


(b) the response time is less than 5 minutes


(c) the response time is more than 10 minutes

Answer 1

Define random variable X : the number of milligrams of porphyrin per deciliter of blood

x is approximately normally distributed with mean = 45 and standard deviation = 14

a)

Here we have to find P(X < 60)

   where z is standard normal variable

  

   (Round to 2 decimal)

= 0.8577 (Statistical table of z values)

Probability that X is less than 60 is 0.8577

b)

Here we have to find P(X > 16)

   where z is standard normal variable

  

   (Round to 2 decimal)

= 1 - P(z < -2.07)

= 1 - 0.0192

= 0.9808 (Statistical table of z values)

Probability that X is greater than 16 is 0.9808

c)

Here we have to find P(16 < X < 60)

  

  

  

= P(z < 1.07) - P(z < -2.07)

= 0.8577 - 0.0192 (From statistical table of z values)

= 0.8385

Probability that X is between 16 and 60 is 0.8385

d)

Here we have to find P(X > 60)

P(X > 60) = 1 - P(X < 60)

= 1 - 0.8577

= 0.1423

Probability that X is more than 60 is 0.1423