statistics math

Question

1. 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 = 41 and standard deviation 𝜎 = 12. Find the following probabilities. (Round your answers to four decimal places.)
2. a) x is less than 60 =
3. b) x is greater than 16=
4. c) x is between 16 and 60=
5. d) x is more than 60 =

Answer 1

Using a Table Of Proportions Of Area Under The Standard Normal Curve:

(a) P(x < 60) is found by computing Z = (x − μ)/σ, here equal to (60 − 41)/12 or 1.583333333. Enter the Table above with the Argument of Z = 1.58 and read a value of P = 0.4429. There is a 0.5 probability that x is less than the given mean of 41. P(x < 60) is then given by (0.5 + 0.4429) or 0.9429.

(b) For P(x > 16), find Z = (x − μ)/σ or (16 − 41)/12 equal to -2.083333333 and enter the Table above with the Absolute Value of -2.08 or |-2.08| or 2.08. The Table will give a value of P = 0.4812. There is a 0.5 probability that x is greater than the given mean of 41. Then obtain P(x > 16) as (0.5 + 0.4812) or 0.9812.

(c) Obtain P(16 < x < 60) by taking the difference of 0.4429 and -0.4812 or 0.9242.

(d) P(x < 60) is given in (a) above as 0.9429. Then P(x > 60) is calculated by 1 − P(x < 60) or

1 − 0.9429 equal to 0.0571.