The International Bottled Water Association says that Americans on the average drink 4.6 (8-oz.) servings of water a day. Assume that the number of 8-oz. servings of water is approximately normally distributed with a standard deviation of 1.4 servings. (Give your answers correct to four decimal places.)

(b) What proportion of Americans drink less than half the recommended 8 servings?

"less than half" = less than 2.3

Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.

z=(8-2.3)/1.4=4.07 graph 0.99998

is this the right way and how do you change the graph numbers since they are all 9's that would need to be rounding?

I worked it and got a different answer for the graph number 0.9893 and tom worked and got something totally different, what are we doing wrong, trying to work together on some of these?

To find the proportion of Americans who drink less than half the recommended 8 servings, we need to calculate the z-score and use the standard normal distribution table.

Step 1: Find the z-score
The z-score formula is: z = (x - μ) / σ
Where:
x = the value we want to find the proportion for (in this case, 4 servings)
μ = the mean (average) number of servings (4.6)
σ = the standard deviation (1.4)

Calculating the z-score:
z = (4 - 4.6) / 1.4
z = -0.4286

Step 2: Use the z-score to find the proportion
We will use the standard normal distribution table or a calculator to find the proportion associated with the z-score. The proportion corresponds to the area under the curve to the left of the z-score.

Using the standard normal distribution table, we find that the proportion associated with a z-score of -0.4286 is approximately 0.3340.

Therefore, the proportion of Americans who drink less than half the recommended 8 servings is approximately 0.3340 or 33.40% (rounded to two decimal places).