In your own words describe the Empirical Rule In what scenarios would you use th

Question

In your own words describe the Empirical Rule In what scenarios would you use the normal distribution and student t distribution to calculate a confidence interval for mu? Explain fully. Upon testing 100 resistors manufactured by Lights-R-Us, it was found that 12 failed to the tolerance specifications. a. Find a 95% confidence interval for the true fraction of resistors manufactured fail to meet the tolerance specification. b. How many resistors should be tested to estimate the true proportion failing to tolerance specifications within 0.05, with confidence coefficient 0.95? One-hour carbon monoxide concentrations in air samples from a large city average 12 with a standard deviation of 9 ppm. Find the probability that the average concentration 100 randomly selected samples will exceed 14 ppm. A structural engineer conducted an experiment on a supply of steel I-beams for a build

Explanation / Answer

1. The Emperical rule states that for a Normal dsitribution, approx 68% of the data falls within first standard deviation from the mean, 95% of the data within 2 standard deviations from the mean and 99.7% of the data within 3 standard deviations from the mean.

2. We use a normal distribution to calculate CI for mean when the standard deviation of the sample is known.

We use a t distribution when the standard deviation of the sample is unknown and we estimate a standard error.

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