Answer:
50%
Step-by-step explanation:
68-95-99.7 rule
68% of all values lie within the 1 standard deviation from mean [tex](\mu-\sigma,\mu+\sigma)[/tex]
95% of all values lie within the 1 standard deviation from mean [tex](\mu-1\sigma,\mu+1\sigma)[/tex]
99.7% of all values lie within the 1 standard deviation from mean [tex](\mu-3\sigma,\mu+3\sigma)[/tex]
The distribution of the number of daily requests is bell-shaped and has a mean of 55 and a standard deviation of 4.
[tex]\mu = 55\\\sigma = 4[/tex]
68% of all values lie within the 1 standard deviation from mean [tex](\mu-\sigma,\mu+\sigma)[/tex] = [tex](55-4,55+4)[/tex]= [tex](51,59)[/tex]
95% of all values lie within the 2 standard deviation from mean [tex](\mu-1\sigma,\mu+1\sigma)[/tex]= [tex](55-2(4),55+2(4))[/tex]= [tex](47,63)[/tex]
99.7% of all values lie within the 3 standard deviation from mean [tex](\mu-3\sigma,\mu+3\sigma)[/tex]= [tex](55-3(4),55+3(4))[/tex]= [tex](43,67)[/tex]
Refer the attached figure
P(43<x<55)=2.5%+13.5%+34%=50%
Hence The approximate percentage of light bulb replacement requests numbering between 43 and 55 is 50%
