Question

Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage.

Answer 1

Answer:

a) 0.923

b) 0.957

c) 0.88

d) 0.077    

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 40

Standard Deviation, σ = 14

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:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P(xis less than 60)

P(x < 60)

$P( x < 60) = P( z < \displaystyle\frac{60 - 40}{14}) = P(z < 1.4285)$

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

$P(x < 60 ) =0.923 = 92.3\%$

b) P(x is greater than 16)

$P(x > 16) = P(z > \displaystyle\frac{16-40}{14}) = P(z > -1.7142)\\\\P( z > -1.7142) = 1 - P(z \leq -1.7142)$

Calculating the value from the standard normal table we have,

$1 - 0.043 = 0.957 = 95.7\%\\P( x > 16) = 95.7\%$

c)P(x is between 16 and 60)

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

$P(16 \leq x \leq 60) = 88\%$

d)  P(x is more than 60)

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