High School

The resistances of ten randomly selected 100-ohm resistors have been recorded: 79.9, 85.9, 87.0, 96.7, 107.4, 100.8, 115.4, 117.9, 98.0, and 102.6. The individual resistances are known to follow a normal distribution with a mean of 100 ohms and a standard deviation of 10 ohms.

(a) Calculate the sample mean resistance associated with the ten resistors.

Answer :

Final answer:

The sample mean resistance of the ten resistors is calculated by summing their individual resistances and dividing by ten, resulting in a sample mean resistance of 99.16 ohms.

Explanation:

To calculate the sample mean resistance of the ten resistors, we add up all the recorded resistances and divide the sum by the total number of resistors.

The resistances are: 79.9, 85.9, 87.0, 96.7, 107.4, 100.8, 115.4, 117.9, 98.0, and 102.6 ohms.

Summing these values gives us:

79.9 + 85.9 + 87.0 + 96.7 + 107.4 + 100.8 + 115.4 + 117.9 + 98.0 + 102.6 = 991.6 ohms

Now, dividing the total resistance by 10 (the number of resistors), we get the sample mean:

991.6 / 10 = 99.16 ohms

Therefore, the sample mean resistance associated with the ten resistors is 99.16 ohms.

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