Question

Example:

We are looking at the cholesterol levels of population of 200 healthy individuals. Cholesterol of the most of individuals is between 190-210mg/dl, with a mean (μ) 200mg/dl and SD (s) 10mg/dl. A study in 10 individuals drawn from same population with cholesterol levels of 180, 200, 190, 180, 220, 190, 230, 190, 190, 180mg/dl gives X̄ = 195 mg/dl and SD (s) = 17.1 mg/dl.

Using the example above solve:

Assign your numbers for mean μ and standard deviation σ.
Then select a number "A" below mean μ, and a number "B" above mean μ.
Use Appendix Table for the Normal Distribution to find the probability
that x is between A and B: P (A < x < B).

Here are steps to follow: convert A to z score (let's call it za),
convert B to z score (let's call it ZB).;
From the Appendix, table find the area under the curve to the left of za and to the left of ZB.
That will give you P (z < za) and P (z < zb).
If za or zb is not in the table, change your A or B.
Use formula: P (A < x < B) = P (za < z < zb) = P (z < zb) - P (z < za)

Answer 1

Question: Assign your numbers for mean μ and standard deviation σ.

= 200

= 10

Question: Then select a number "A" below mean μ, and a number "B" above mean μ.

Answer:
Select

A = 190

B = 210

Question: Use Appendix Table for the Normal Distribution to find the probability
that x is between A and B: P (A < x < B).

Step 1: convert A to z score (let's call it zA),

Z_A = (190 - 200)/10

   = - 1.00

Step 2: convert B to z score (let's call it zB),

Z_B = (210 - 200)/10

   = 1.00

Step 3: From the Appendix, table find the area under the curve to the left of za and to the left of ZB.
That will give you P (z < za) and P (z < zb).

P(Z < Z_A) = 0.1587

P(Z < Z_B) = 0.8413

Step 4: Use formula: P (A < x < B) = P (za < z < zb) = P (z < zb) - P (z < za)

P(A < X < B) = 0.8413 - 0.1587 = 0.6826