A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 197.4-cm and a standard deviation of 1.6-cm. For shipment, 13 steel rods are bundled together.Find the probability that the average length of a randomly selected bundle of steel rods is greater than 198.5-cm.P(M > 198.5-cm) =

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Asked Nov 4, 2019
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A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 197.4-cm and a standard deviation of 1.6-cm. For shipment, 13 steel rods are bundled together.

Find the probability that the average length of a randomly selected bundle of steel rods is greater than 198.5-cm.
P(M > 198.5-cm) = 

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Expert Answer

Step 1

Given data

Mean = 197.4 cm

Standard deviation = 1.6 cm

Sample size n = 13

probability that the average leng...

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P(M 198.5) Changing into standard normal variate 198.5 197.4 Pz> = P(z > 2.4788) 1.6 13 1 - P(z P(z > 2.4788) 2.4788) = 1 - 0.9934 = 0.0066 (P(z 2.4788) = 0.9934(From Excel NORM. S. DIST(2.4788, TRUE))

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