A contractor involved in high-rise building construction orders thousands of ste

Question

A contractor involved in high-rise building construction orders thousands of steel rods each year from a supplier. The strength, X, of the rods is a normally distributed random variable. When a shipment arrives, the contractor selects a random sample of 15 rods and determines the sample mean strength and the sample standard deviation. These results are then used to compute a confidence interval for the population mean strength of the rods.

4. For a particular shipment, the sample mean strength of the selected rods is 990 pounds and the sample standard deviation is 14.5 pounds. What is the margin of error for a 95% confidence interval for the population mean strength?

(a) 7.98 pounds (b) 2.07 lbs. (c) 8.03 lbs. (d) 7.34 lbs. (e) 8.31 lbs.

Explanation / Answer

Margin of error is given as z*SE

for 95% confidence, the z value is 1.96

also SE is s/sqrt(N)=14.5/sqrt(15)=3.744

thus z*SE is 1.96*3.744=7.34 . thus option D

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