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Chapter 9: Problem 35

Acrylic bone cement is sometimes used in hip and knee replacements to fix an artificial joint in place. The force required to break an acrylic bone cement bond was measured for six specimens under specified conditions, and the resulting mean and standard deviation were \(306.09\) Newtons and \(41.97\) Newtons, respectively. Assuming that it is reasonable to assume that breaking force under these conditions has a distribution that is approximately normal, estimate the true average breaking force for acrylic bone cement under the specified conditions.

Short Answer

Expert verified
The true average breaking force for acrylic bone cement under the specified conditions is estimated to be \(306.09\) Newtons.

Step by step solution

01

Identify the Given Information

In the given problem, we know that the mean force required to break an acrylic bone cement bond for six specimens under specified conditions is \(306.09\) Newtons, and the standard deviation is \(41.97\) Newtons.
02

Analyzing the Information

Because we're dealing with a normal distribution and have been given the sample mean and standard deviation, we can infer that we have a good estimate of the population mean. The Central Limit Theorem implies that for sufficiently large sample sizes, the distribution of the sample mean is approximately normal, regardless of the shape of the population distribution.
03

Estimating the True Average Force

The true average breaking force of the acrylic bone cement, assuming a normal distribution, is given by the sample mean, which is \(306.09\) Newtons. This estimation is based on the sample data we have and the assumption that the breaking force has a normal distribution.

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