Question

an adult has on average 6.2 liters of blood. assume the variable is normally distributed and has a standard deviation of 0.3. find the probability that a person has less than 5.4 liters of blood.

Answer 1

Let X be the variable denoting the liters of blood an adult has.

X N(6.2,0.3²) ,

where = E[X] = 6.2 and ² = Var[X] = 0.3² = 0.09

Z =( X - ) / N(0,1)

Pr[ X < 5.4 ] = Pr[ (X -  ) / < (5.4-6.2)/0.3 ] = Pr[Z < -2.6667 ] =

= 1 -  

= 1 - 0.6064199

= 0.3935801 0.3936       [ correct up to 4 decimal places ]