A company produces steel rods. The lengths of the steel rods are
normally distributed with a mean of 136.9-cm and a standard
deviation of 2.2-cm. For shipment, 29 steel rods are bundled
together.
Find the probability that the average length of a randomly selected
bundle of steel rods is between 137.8-cm and 138.1-cm.
P(137.8-cm < M < 138.1-cm) =
Enter your answer as a number accurate to 4 decimal places. Answers
obtained using exact z-scores or z-scores rounded
to 3 decimal places are accepted.
We are taking a sample of 29 rods out of the population with
Population Mean() 136.9, Population Standard Deviation() 2.2.
For the sampling distribution, Mean is equal to the population mean.
Sample Standard Deviation of Sample(S)= population standard deviation()/ = 2.2/= 0.40853
Standardizing the sampling distribution:
Z=
Z stat for (x=137.8)= (137.8-136.9)/0.40853= 2.203022
Z stat for (x=138.1)=(138.1-136.9)/0.40853=2.937363
Using Z stat table,
P(2.203022<x<2.937363) = 0.012142
Therefore , the probability that the average length of a randomly selected bundle of steel rods is between 137.8-cm and 138.1-cm.= 0.0121
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