Question

Medical: Blood Protoplasm Porphyrin is a pigment in blood protoplasm and other body uids that is signicant 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 adults, x is approximately normally distributed with mean μ = 41 and standard deviation σ = 9. What is the probability thata) x is less than 55?

Answer 1

Answer:

0.9401 is the required probability.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 41

Standard Deviation, σ = 9

We are given that the distribution of number of milligrams of porphyrin is a bell shaped distribution that is a normal distribution.

Formula:

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

P(x is less than  55)

$P( x < 55) = P( z < \displaystyle\frac{55 - 41}{9}) = P(z < 1.556)$

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

$P(x < 55) =0.9401 =94.01\%$

0.9401 is the probability that x is less than 55.