Identify the underlying issue/problem Formulate a methodology to solve the issue

Question

Identify the underlying issue/problem

Formulate a methodology to solve the issue/problem

Elaborate in a paragraph why this methodology is appropriate to solve the problem.

Briefly state the data you would gather to apply the statistical method

JJ fits normal density function to his tensile strength data and finds that it fits well. He has 2048 individual tensile strength data from which he calculates the sample mean and sample variance. Using these two values how he will find the low and high value of tensile strength that includes the middle 68% of the data set. That is the low and high values are symmetric from the midpoint.

Explanation / Answer

Here the data fits to normality so we can use empirical rule. The empirical rule tells that,

68% of data lie within the first standard deviation from the mean.

95% of data lie within two standard deviations.

99.7% of data lie within three standard deviations.

He has sample mean and sample variance. If we do the square root for sample variance then we get the sample standard deviation.

For middle 68% the low value = sample mean – sqrt (sample variance)

                                   high value = sample mean + sqrt (sample variance)

Here the sample size is large 2048 this support the normality assumption and already we found that the parent population fits for normality so empirical rule is appropriate here. Here the person is using empirical rule to find the low and high value. This methodology is appropriate to solve this problem.

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