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

0.9401 is the required probability.

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(x-\mu)/(\sigma)`

P(x is less than 55)

`P( x < 55) = P( z < \displaystyle(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.