The volume of soft drink in plastic bottles is a normal random variable with mean 16 ounces and standard deviation 0.7 ounces.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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The volume of soft drink in plastic bottles is a normal random variable with mean 16 ounces and
standard deviation 0.7 ounces.
(a) If a bottle is selected at random, find the probability that it contains more than 15.3 ounces of
soft drink. (Round your answer to four decimal places.)
(b) A random sample of 25 bottles is selected from a large quantity of filled bottles. According to the
Central Limit theorem,
i. What is the mean of the distribution of sample means?
ounces
ii. What is the standard deviation of the distribution of sample means? (Round your answer to
two decimal places)
ounces](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F78433f83-59df-4715-980e-f38858e2923c%2F78e98e92-4138-4462-893e-ab1ea34da01b%2F1vawlx4_processed.jpeg&w=3840&q=75)
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(c) Find the probability that the mean volume of soft drink in the 25 sampled bottles is less than 15.3
ounces (Round your answer to three decimal places)
(d) Find the probability that the mean volume of soft drink in the 25 sampled bottles is more than
15.5 ounces. (Round your answer to three decimal places)
Submit Question](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F78433f83-59df-4715-980e-f38858e2923c%2F78e98e92-4138-4462-893e-ab1ea34da01b%2Fefs31zr_processed.jpeg&w=3840&q=75)
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