Answer to Question #181723 in Statistics and Probability for drittany

Question

The average cholesterol content of a certain duck eggs is 210 milligrams, and the standard deviation is 16 milligrams. Assume the variable is normally distributed.

If a single egg is selected at random, what is the probability (in decimal) that the cholesterol content will be greater than 205 milligrams?

Answer 1

The probability that X > 205 is equal to the blue area under the curve.

Since $\mu$ = 210 and $\sigma = 16$  we have:

P( X > 205 ) = P(X - $\mu$ > 205 - 210) = P$(\frac{X-\mu}{\mu} > \frac{205-210}{16} )$

Since $Z = \frac{X-\mu}{\sigma}$ and $\frac{205-210}{16} = -0.31$ we have:

P( X > 205) = P( Z > -0.31)

Use the standard normal table to conclude that:

P( Z > -0.31) = 1 - 0.3783 = 0.6217

We can do such manipulation because in the table there is the area to the left of z-score, but area to the right is 1-(area to the left)

Answer: P = 0.6217.

P.S. Here's the standard normal table: