The banking industry has suffered in recent years because of a high default rate on energy-related loans.The standard deviation is $10,000.How large a sample must you take from banking records to be 98% confident that your estimate for the amount of these defaults is within $1000 of the true mean loan amount?
A) 567
B) 233
C) 240
D) 543
E) 890

Question

Quizplus · Accepted Answer

We need to use the formula n = (z*σ/E)^2, where n is the sample size, z is the z-score for a 98% confidence interval (2.33), σ is the standard deviation ($10,000), and E is the margin of error ($1000). 
Plugging in the values, we get n = (2.33*10,000/1000)^2 = 543. Therefore, we need a sample size of 543 to be 98% confident that our estimate for the amount of energy-related loan defaults is within $1000 of the true mean loan amount.

The Banking Industry Has Suffered in Recent Years Because of a High