Problem 13E

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

i. less than 5 Ω

ii. greater than 5 Ω

iii. equal to 5 Ω

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.)

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.