The average mass of a freight car is 5634.5 kg with a standard deviation of 642

Question

The average mass of a freight car is 5634.5 kg with a standard deviation of 642 kg. What is the probability that a sample of size 100 will have an average mass between 5600 and 5700 kg? Give your answer to four decimal places. The average mass of a freight car is 5634.5 kg with a standard deviation of 642 kg. What is the probability that a sample of size 100 will have an average mass between 5600 and 5700 kg? Give your answer to four decimal places. The average mass of a freight car is 5634.5 kg with a standard deviation of 642 kg. What is the probability that a sample of size 100 will have an average mass between 5600 and 5700 kg? Give your answer to four decimal places.

Explanation / Answer

Given : = 5634.5 = 642

n = 100

P(5600 < x' < 5700)

= P((5600 - 5634.5) / 642 * 100 < x' < (5700 - 5634.5) / 642 * 100)

= P(-0.5374 < x' < 1.0202)

= P(x' < 1.0202) - P(x' < -0.5374)

Using z tables,

= 0.8462 - 0.2955

= 0.5507.

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