SOLUTION: A local bank has determined that the daily balances of the checking accounts of its customers are normally distributed with an average of $280 and a standard deviation of $20. Q

Question 1121170: A local bank has determined that the daily balances of the checking accounts of its customers are normally distributed with an average of $280 and a standard deviation of $20.
Questions:
1. What percentage of its customers has daily balances of more than $275?
2. What percentage of its customers has daily balances less than $243?
3. What percentage of its customers' balances is between $241 and 301.60?
Please show with narrative on how you arrived with the answers and explain the process.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Need a z-score with all of these, which essentially makes the table needed a standard normal table with mean 0 and sd 1
z=(x-mean)/sd
a. (275-280)/20=-0.25
want the probability of z <-0.25, and that is 0.4013 or 40.13%
b.(243-280)/20=-1.85, and probability of z < -1.85 is 0.0322 or 3.22%
c. this is z of -39/20 or -1.95 and z of 21.60/20 or 1.08. This has a probability of 0.8343 or 83.43%
Use 2nd VARS 2 for normal cdf and put in the numbers, with at least -6 or +6 for minus or plus infinity. 1E99 is fine but isn't really necessary.
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