For Emily's birthday, her father treated her and five friends to a dinner at a restaurant at the mall. Emily and her friends ord
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Answer:
Question 4: 20 + 6 + 6 + 12 + 16 = 60
Question 5: 144 + 90 + 90 + 48 + 48 = 420
Question 6: 78.28 + 78.28 + 88.58 + 27.09 + 27.09 = 299.32
Step-by-step explanation:
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Answer:
27.43% probability that the mean volume of a random sample of 144 bottles is less than 12 oz.
Step-by-step explanation:
To solve this problem, it is important to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
What is the probability that the mean volume of a random sample of 144 bottles is less than 12 oz
This is the pvalue of Z when
By the Central Limit Theorem
has a pvalue of 0.2743.
So there is a 27.43% probability that the mean volume of a random sample of 144 bottles is less than 12 oz.