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=14.
Find the following probabilities.
a) xis less than 60
b) x is greater than 16
c) x is between 16 and 60
d) x is more than 60

We are given that the distribution of number of milligrams of porphyritic per deciliter of blood is a bell shaped distribution that is a normal distribution.

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

a) P(xis less than 60)

P(x < 60)

[tex]P( x < 60) = P( z < \displaystyle\frac{60 - 40}{14}) = P(z < 1.4285)[/tex]

Calculation the value from standard normal z table, we have,

[tex]P(x < 60 ) =0.923 = 92.3\%[/tex]

b) P(x is greater than 16)

[tex]P(x > 16) = P(z > \displaystyle\frac{16-40}{14}) = P(z > -1.7142)\\\\P( z > -1.7142) = 1 - P(z \leq -1.7142)[/tex]

Calculating the value from the standard normal table we have,

[tex]1 - 0.043 = 0.957 = 95.7\%\\P( x > 16) = 95.7\%[/tex]

c)P(x is between 16 and 60)

[tex]P(16 \leq x \leq 60) = P(\displaystyle\frac{16 - 40}{14} \leq z \leq \displaystyle\frac{60-40}{14}) = P(-1.7142 \leq z \leq 1.4285)\\\\= P(z \leq 1.4285) - P(z < -1.7142)\\= 0.923 - 0.043= 0.88 = 88%[/tex]

[tex]P(16 \leq x \leq 60) = 88\%[/tex]

d) P(x is more than 60)

P(x > 60) = 1 - P(x < 60) = 1 - 0.923 = 0.077