The director for operations for the State Bank and Trust recently performed a st
ID: 3070210 • Letter: T
Question
The director for operations for the State Bank and Trust recently performed a study of the time bank customers spent from the moment they arive in the parking lot until they excted the front door after completing banking business. Data from a random sample of 1062 customers over a 4-week period revealed a unimodal and symmetric shape, with a mean of 21.4 minutes and a standard deviation of 4 minutes (a) what is the more for time of 25,4 minutes? CUse 3 decima' places.) ooo (b) A manager at one branch has decided to give a gift certificate to a local restaurant to any customer who is required to spend more than 33.4 minutes in the service process. Use the 68-95-99.7 Rule to approximate what percent or customers wil receive a gift certificate. (Enter as a pecent, to 2 decemal places.) 0.15] % (a) (25.4-214)/4-1.000 (b) The waue 3,4 i, exac, J standard d v ations above the mean, so there is 99.7% inside the terva and 3% outside, sp t equally between helo er and 15% on each side. per ta sExplanation / Answer
When we use a standard normal model in statistics:
1. about 68% of values fall within one standard deviation of the mean i.e. in this case 68% values fall in (21.4-3,21.4+3) ie. (18.4,24.4)
2. about 95% of the values fall within two standard deviations from the mean i.e. in this case 95% value fall in (21.4-2x3,21.4+2x3) ie. (15.4, 27.4)
3. lmost all of the values i.e. about 99.7% fall within three standard deviations from the mean i.e. in this case 99.7% values fall in (21.4-3x3,21.4+3x3) ie. (12.4, 30.4)
These facts are what is called the 68-95-99.7 rule, sometimes called the Empirical Rule.
Hence outside the interval (12.4, 30.4), (100-99.7)%=0.3% values fall. If we split equally bothsides (since normal distribution is symmetric about mean) then approximate percentage of customers who spend more than 33.4 mintues in the service process will receive a gift certificate=(0.3)/2%=0.15%