Question

an important problem in industry is shipment damage. a windshield factory ships its product by truck and determines that it cannot meet its profit expectations if, on average, the number of damaged items per truckload is greater than 12. a random sample of 12 departing truckloads is selected at the delivery point and the average number of damaged items per truckload is calculated to be 9.4 with a calculated sample of variance of 0.64. select a 99% confidence interval for the true mean of damaged items.

Answer 1

99% confidence interval would be (10.78,11.82) for the true mean of the damaged items.

What is meant by Variance?

Variability is measured by the variance. It is determined by averaging the squared deviations from the mean.

The degree of dispersion in your random sample collection is indicated by variance. The variance is greater in respect to the mean the more dispersed the data.

You may determine the average distance between each number and the mean using the standard deviation, which is obtained from variance. It is the variance's square root.

Both metrics capture distributional variability, although they use different measurement units:

Standard deviation is represented in the same units as the initial values (e.g., meters).

Larger units are used to express variation.

How to solve?

n = 12

Average = 11.3

Variance = 0.49

Standard deviation = √0.49=0.7

so, we need to find 99% confidence interval.

At 99% confidence , z = 2.58

So, interval would be

x±z* σ/√n = 11.3 ±2.58* 0.7/√12

=11.3±0.521

=(11.3 - 0.521,11.3 +0.521

= (10.78, 11.82)

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