SOLUTION: Water bottle weights are normally distributed with a mean of 16 ounces and a standard deviation of 0.7 ounces. What is the probability that a water bottle contains at most 16 ounce

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Question 847365: Water bottle weights are normally distributed with a mean of 16 ounces and a standard deviation of 0.7 ounces. What is the probability that a water bottle contains at most 16 ounces? Enter your answer as a decimal rounded to the nearest thousandths place.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

Demonstrating Using TI Calculator

The syntax is normalcdf(smaller, larger, µ, σ).

Note: The -9999 is used as the smaller value to be at least 5 standard deviations from the mean.

P(x ≤ 16) = normalcdf(-9999, 16, 16, .7) = .5

For the normal distribution: 

one  standard deviation from the mean accounts for about 68.2% of the set 

two standard deviations from the mean account for about 95.4%

and three standard deviations from the mean account for about 99.7%.

Important to Understand z -values as they relate to the Standard Normal curve:

Below:  z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.  

Note: z = 0 (x value the mean) 50% of the area under the curve is to the left and 50% to the right