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marta [7]
3 years ago
15

An important problem in industry is shipment damage. A windshield factory ships its product by truck and determines that it cann

ot 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.
Mathematics
1 answer:
Sunny_sXe [5.5K]3 years ago
7 0

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).

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