Question

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 153.6 cm and a standard deviation of 2.1 cm. For shipment, 13 steel rods are bundled together.

Note: Even though our sample size is less than 30, we can use the z score because
1) The population is normally distributed and
2) We know the population standard deviation, sigma.

Find the probability that the average length of a randomly selected bundle of steel rods is between 154.5 cm and 155.4 cm.


Enter your answer as a number accurate to 4 decimal places.

Answer 1

X : lengths of the steel rods

X ~ ( 153.6 , 2.1)

13 steel rods are bundled together., so, sample size (n) = 13

the mean length of the sample will follow normal distribution with :-

the probability that the average length of a randomly selected bundle of steel rods is between 154.5 cm and 155.4 cm is :-

[ in any blank cell of excel type =NORMSDIST(3.0905) press enter ]

[ in any blank cell of excel type =NORMSDIST(1.5452) press enter ]

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