Mean=15.854, Median=15.99, Mode=16.21, SD=0.661381
1) what is the probability that a randomly chosen bottle will contain 16 ounces of soda? 0.22075, 0.587357
2)What is the value of soda associated with a Zscore of -1.5
1) 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.
2) Insert values into above equation and solve for score.
To find the probability that a randomly chosen bottle will contain 16 ounces of soda, we can use the concept of a normal distribution and the given statistics.
1) First, we need to calculate the Z-score of 16 ounces.
Z-score = (X - Mean) / Standard Deviation
Z-score = (16 - 15.854) / 0.661381
Z-score = 0.22075 (rounded to 5 decimal places)
2) The probability corresponding to a particular Z-score can be found using a Z-table (also known as a standard normal distribution table). You can find this table online or use statistical software that provides Z-score calculations.
Looking up the Z-score of 0.22075 in the Z-table, the corresponding probability is approximately 0.587357 (rounded to 6 decimal places).
Therefore, there is a probability of approximately 0.587357 (or 58.74%) that a randomly chosen bottle will contain 16 ounces of soda.
2) To find the value of soda associated with a Z-score of -1.5, we can use the inverse of the Z-score formula.
X = (Z-score * Standard Deviation) + Mean
X = (-1.5 * 0.661381) + 15.854
X = 14.8402375 (rounded to 4 decimal places)
Therefore, the value of soda associated with a Z-score of -1.5 is approximately 14.8402 ounces.