SOLUTION: 1. Company records show that the weekly distance travelled by their salesmen is approximately normally distributed with mean 800 miles and standard deviation 90 miles. The sales ma

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Question 856911: 1. Company records show that the weekly distance travelled by their salesmen is approximately normally distributed with mean 800 miles and standard deviation 90 miles. The sales manager considers that salesman who travel less than 600 miles in one week are performing poorly.
(a) If the company employs 200 salesmen, how many would be expected to perform poorly in a particular week ? (approximately 3)
(b) The sales manager wishes to identify the number of miles travelled in one week, above which only 1% of salesmen are expected to exceed. What weekly mileage is this? (1009.7 miles)
# the answer has been provided in the bracket. i would like to know the solution. thank you very much.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

mean 800 miles and standard deviation 90 miles. 

Percentage who preform poorly:  z=%28600-800%29%2F90 = -2.222, NORMSDIST(-2.222) = .0131

a) 200*.0131 = 2.62  0r ~3

b)|NORMSINV(.01)| = 2.3263 = %28X-800%29%2F90, X = 1009.367 = 1009.4

For the normal distribution: 

one  standard deviation from the mean accounts for about 68.2% of the set 

two standard deviations from the mean account for about 95.4%

and three standard deviations from the mean account for about 99.7%.

Important to Understand z -values as they relate to the Standard Normal curve:

Below:  z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.  

Note: z = 0 (x value the mean) 50% of the area under the curve is to the left and %50 to the right