Question

Assume that the red blood cell counts of woman are normally distributed with a mean of 4.577 and a standard deviation of 0.328. Apply technology or calculator to solve the following questions, make sure you apply the round-off rule correctly:

(a) Find the probability that a randomly selected woman has a red blood cell count below the normal range of 4.1 to 5.4.

(b) Find the probability that a randomly selected woman has a red blood cell count above the normal range of 4.1 to 5.4.

Answer 1

We are given the distribution here as:

a) Now the probability that a randomly selected woman has a red blood cell count below the normal range of 4.1 to 5.4, is computed here as:

P( 4.1 < X < 5.4) = P(X < 5.4) - P(X < 4.1)

As we are allowed to use anything here, we will use EXCEL to compute the above probability here as:

=NORM.DIST(5.4,4.577,0.328,TRUE)-NORM.DIST(4.1,4.577,0.328,TRUE)

The output here is 0.9210

Therefore 0.9210 is the required probability here.

b) Now the probability that a randomly selected woman has a red blood cell count above the normal range of 4.1 to 5.4.

P(X > 5.4)

This is computed in EXCEL here as:
=1-norm.dist(5.4,4.577,0.328,TRUE)

The output here is 0.0061

Therefore 0.0061 is the required probability here.