He physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 40 and a standard deviation of 7. Using the 68-95-99.7 (Empirical) Rule, what is the approximate percentage of lightbulb replacement requests numbering between 40 and 47

the approximate percentage of light bulb replacement requests numbering between 40 and 47 is 34% .

Step-by-step explanation:

Step 1: Sketch the curve.

The probability that 40<X<47 is equal to the blue area under the curve.

Step 2:

Since μ=40 and σ=7 we have:

P ( 40<X<47 ) = P ( 40−40 < X−μ < 47−40 )=P ( 40−40/7< X−μ/σ < 47−40/7)

Since Z = x−μ/σ , 40−40/7 = 0 and 47−40/7 = 1 we have:

P ( 40<X<47 )=P ( 0<Z<1 )

Step 3: Use the standard normal table to conclude that:

P ( 0<Z<1 )=0.3413

Percentage = 0.3413(100)=34.13%

Therefore , the approximate percentage of light bulb replacement requests numbering between 40 and 47 is 34% .

b. astronomers