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 53 and a standard deviation of 11. Using the empirical rule (as presented in the book), what is the approximate percentage of daily phone calls numbering between 31 and 75?
Can you explain this for me too please

Answer 1

Solution :

Given that ,

mean = $\mu$ = 53

standard deviation = $\sigma$ = 11

P(31 < x < 75) = P[(31 - 53)/ 11) < (x - $\mu$ ) /$\sigma$  < (75 - 53) / 11) ]

= P(-2 < z < 2)

= P(z < 2) - P(z < -2)

= 0.9772 - 0.0228

= 0.9544

percentage = 95.44%