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 11.3 with a calculated sample of variance of 0.49. Select a 99% confidence interval for the true mean of damaged items.

Answer 1

Answer:  99% confidence interval would be (10.78,11.82).

Step-by-step explanation:

Since we have given that

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

$\bar{x}\pm z\dfrac{\sigma}{\sqrt{n}}\\\\=11.3\pm 2.58\times \dfrac{0.7}{\sqrt{12}}\\\\=11.3\pm 0.521\\\\=(11.3-0.521,11.3+0.521)\\\\=(10.78,11.82)$

Hence, 99% confidence interval would be (10.78,11.82).