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In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 47 and a standard deviation of 3. Using the empirical rule, what is the approximate percentage of daily phone calls numbering between 41 and 53? Do not enter the percent symbol.

Answer :

DN445go
Prob ( 41 = X = 77) =

Prob ( (41-59)/9 = Z = (77-59)/9 ) = --- changes to z scores

Prob ( -18/9 = Z = 18/9 ) =

Prob ( -2 = Z = 2) =

Prob ( z=2) - Prob(Z=-2) = by property of the normal bell curve

= 0.9772 - 0.0228 per the normal distribution table

= 0.9544

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