Can someone break this down for me please?

Question

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 64 and a standard deviation of 4. Using the empirical rule (as presented in the book), what is the approximate percentage of daily phone calls numbering between 52 and 76?

Answer 1

64-52=12= 3x4 standard deviations below the mean

76-64= 12= 3x4 standard deviations above the mean

by the empirical rule 99.7% (sometimes they just use 99% which is nearly 100% either way) of the area under a normal curve is within

3 standard deviations from the mean

99.7% of the daily phone calls are between 52 and 72

that's an approximation, but very accurate approximation

to get an even better approximation, use z tables or an online or handheld statistics calculator. the z scores are from -3 to +3 for 52 to 76. 99.73% is an even more accurate percentage of the calls between 52 and 76, found by pluggin the numbers into an online z calculator

z score = (raw score- mean)/standard deviation

z for 52 = (52-64)/4 = -12/4 =-3

z for 76 =(76-64)/4 = 12/4 = 3