A sample of 100 resistors has an average resistance of \(50\ \Omega\) and a standard deviation of \(5\ \Omega\). A second sample of 100 resistors has an average resistance of \(100\ \Omega\) and a standard deviation of \(5\ \Omega\). If the two samples are combined, the standard deviation of all 200 resistances will be .

i. less than \(5\ \Omega\)

ii. greater than \(5\ \Omega\)

iii. equal to \(5\ \Omega\)

iv. can’t tell from the information given

(Hint: Don’t do any calculations. Just try to sketch,

very roughly, histograms for each sample separately,

then for the combined sample.)

Equation Transcription:

Text Transcription:

50 ohms

5 ohms

100 ohms

5 ohms

5 ohms

5 ohms

Answer :

Step 1 of 2 :

Given, a sample of 100 resistors are taken, where, average is 50 and standard deviation is 5.

From another sample of 100 resistors has an average resistance of 100 and a standard deviation of 5.

if two samples are combined, The claim to suggest one of the standard deviation given below

(i) less than 5

(ii) greater than 5

(iii) equal to 5

(iv) can’t tell from the information given.