Answer: a) 0.9332, b) 0.8944
Step-by-step explanation: the probability value attached to a z score is gotten by using a z distribution table.
The z score is gotten by making use of the formulae below
Z = x - u / σ
Where x = sample mean, u = population mean and σ = population standard deviation.
a)
For our question, u = 38, σ = 12, we are to look for the z score at z ≤ 56, that's x = 56
By substituting the parameters, we have that
z ≤ 56 = 56 - 38/ 12
z ≤ 56 = 18/12
z ≤ 56 = 1.5
To get the probabilistic value, we check the normal distribution table.
The table I'm using will be giving me probabilistic value towards the left of the area.
From the table, p ( z ≤ 56) = 0.9332.
b)
Z >23 = 23 - 38/ 12
Z >23 = - 15/ 12
Z >23 = - 1.25
The probability value of this z score is towards the right of the distribution but the table I'm using is only giving probability values towards the left.
Hence Z >23 = 1 - Z<23
From the table, Z<23 = 0.1056.
Z >23 = 1 - 0.1056
Z >23 = 0.8944
Answer:
A) P(X < 56) = 0.9332
B) P(X > 56) = 0.8944
Step-by-step explanation:
From the 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.
x is approximately normally distributed with;
mean μ = 38
standard deviation σ = 15.
So the distribution of X is written as:
X ~ N (μ = 38, σ = 15)
A) The required probability that x is less than 56 is given as;
P(X < 56) = P((x - μ)/σ) < (56-38)/15)
Thus, we have;
P(z ≤ 1.5)
From the table attached, it gives a value of; 0.93319 ≈ 0.9332
B)The required probability that x is greater than 23 is given as;
P(X > 56) = P((x - μ)/σ) < (23-38)/12)
Thus, we have;
P(z ≥ -1.25) = 1 - P(z ≤ -1.25)
From the second table attached,
P(z ≥ -1) = 1 - 0.10565 = 0.89435 ≈ 0.8944
