Porphyrin is a pigment in blood protoplasm and other body fluids that is signifi
ID: 3057130 • Letter: P
Question
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 = 39 and standard deviation = 15. Find the following probabilities. (Round your answers to four decimal places.)
(a) x is less than 60
(b) x is greater than 16
(c) x is between 16 and 60
(d) x is more than 60 (This may indicate an infection, anemia, or another type of illness.)
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Consider a normal distribution with mean 28 and standard deviation 3. What is the probability a value selected at random from this distribution is greater than 28? (Round your answer to two decimal places.)
Explanation / Answer
Q1.
the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 39
standard Deviation ( sd )= 15
a.
LESS THAN
P(X < 60) = (60-39)/15
= 21/15= 1.4
= P ( Z <1.4) From Standard Normal Table
= 0.9192
b.
GREATER THAN
P(X > 16) = (16-39)/15
= -23/15 = -1.5333
= P ( Z >-1.5333) From Standard Normal Table
= 0.9374
c.
BETWEEN THEM
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 16) = (16-39)/15
= -23/15 = -1.5333
= P ( Z <-1.5333) From Standard Normal Table
= 0.0626
P(X < 60) = (60-39)/15
= 21/15 = 1.4
= P ( Z <1.4) From Standard Normal Table
= 0.9192
P(16 < X < 60) = 0.9192-0.0626 = 0.8566
d.
GREATER THAN
P(X > 60) = (60-39)/15
= 21/15 = 1.4
= P ( Z >1.4) From Standard Normal Table
= 0.0808
Q2.
the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 28
standard Deviation ( sd )= 3
GREATER THAN
P(X > 28) = (28-28)/3
= 0/3 = 0
= P ( Z >0) From Standard Normal Table
= 0.5