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Example 7-1 Resistors An electronics company manufactures resistors that have a mean resistance of 100 ohms and a standard deviation of 10 ohms. The distribution of resistance is normal. Find the prob- ability that a random sample of n = 25 resistors will have an average resistance of fewer than 95 ohms. Note that the sampling distribution of X is normal with mean µx = 100 ohms and a standard deviation of Central Limit Theorem If X₁, X₂, ..., X, is a random sample of size n taken from a population (either finite or infinite) with mean μ and finite variance o² and if X is the sample mean, the limiting form of the distribution of Z= X-μ o/ √n (7-1) as n→∞, is the standard normal distribution.

Example 7-1 Resistors An electronics company manufactures resistors that have a mean resistance of 100 ohms and a standard deviation of 10 ohms. The distribution of resistance is normal. Find the prob- ability that a random sample of n = 25 resistors will have an average resistance of fewer than 95 ohms. Note that the sampling distribution of X is normal with mean µx = 100 ohms and a standard deviation of Central Limit Theorem If X₁, X₂, ..., X, is a random sample of size n taken from a population (either finite or infinite) with mean μ and finite variance o² and if X is the sample mean, the limiting form of the distribution of Z= X-μ o/ √n (7-1) as n→∞, is the standard normal distribution.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 26PFA
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Example 7-1 Resistors An electronics company manufactures resistors that have a mean resistance of 100 ohms and a standard deviation of 10 ohms. The distribution of resistance is normal. Find the prob- ability that a random sample of n = 25 resistors will have an average resistance of fewer than 95 ohms. Note that the sampling distribution of X is normal with mean µ = 100 ohms and a standard deviation of Central Limit Theorem If X₁, X₂, ..., X, is a random sample of size n taken from a population (either finite or infinite) with mean μ and finite variance o² and if X is the sample mean, the limiting form of the distribution of Z= X-μ o/ √n (7-1) as n→∞, is the standard normal distribution.
Transcribed Image Text:Example 7-1 Resistors An electronics company manufactures resistors that have a mean resistance of 100 ohms and a standard deviation of 10 ohms. The distribution of resistance is normal. Find the prob- ability that a random sample of n = 25 resistors will have an average resistance of fewer than 95 ohms. Note that the sampling distribution of X is normal with mean µ = 100 ohms and a standard deviation of Central Limit Theorem If X₁, X₂, ..., X, is a random sample of size n taken from a population (either finite or infinite) with mean μ and finite variance o² and if X is the sample mean, the limiting form of the distribution of Z= X-μ o/ √n (7-1) as n→∞, is the standard normal distribution.
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