PVC pipe is manufactured with a mean diameter of 1.01 inch and a standard deviation of 0.003 inch. The diameters are known to be normally distributed. 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. (Express the final answer to four decimal places (e. g. 0.9876).)

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.

answer:

1. 0.04

2. 0.15

step-by-step explanation:

i just finished that assignment for properties of probability distributions.

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this is the answer for you hope it