kenny made pillows to sell at the fair. He paid $175.96 for supplies. He charged $8.75 for each pillow sold. Kenny sold 27 pillo
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Answer:
0.8185
Step-by-step explanation:
To solve this question, we have to understand the normal probability ditribution and the central limit theorem.
Normal probability distribution:
Problems of normally distributed samples can be 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
, the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
Find the probability that a random sample of n = 9 sections of pipe will have a sample mean diameter greater than 1.009 inch and less than 1.012 inch.
This is the pvalue of Z when X = 1.012 subtracted by the pvalue of Z when X = 1.009. So
X = 1.012
By the Central limit theorem
has a pvalue of 0.9772
X = 1.009
has a pvalue of 0.1587
0.9772 - 0.1587 = 0.8185
0.8185 = 81.85% probability that a random sample of n = 9 sections of pipe will have a sample mean diameter greater than 1.009 inch and less than 1.012 inch.