Answered

Recall that the RA Company has 100 branches nationwide and its annual profit of RA Company is normally distributed with a mean of P73 million a year and standard deviation of P3.25 million. What percentage of its branches have a profit of P73 million and P80 million?

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Answer:

Note: (What is asked is P73 and P80 million but what I have solution for is P73 to P80 million)

48.42% is the percentage of the branches that has a profit of P73 million to P80 million

Step-by-step explanation:

The given is as follows;

μ = 73

σ = 3.25

The formula for Z-Score is;

Z = X-μ/σ

X = 73;

Z = 73-73/3.25

Z = 0/3.25

Z = 0.00

By look at the table of z-scores 0 has an area of 0

X = 80;

Z = 80-73/3.25

Z = 7/3.25

Z = 2.15 (rounded up)

By looking at the z-score table the area for 2.15 is 0.4842

By drawing the normal curve, draw a vertical line on 0 for z=0 and draw a vertical line on 0.4842 for z=2.15

We can find the area between the z scores of 0 and 2.15 by subtracting;

0.4842 - 0 = 0.4842

So, the area between the z-scores of 0 and 2.15 is 0.4842

what percentage is asked so we can simply multiply 0.4842 to 100 to get 48.42%

therefore, 48.42% is the percentage of the branches that has a profit of P73 million to P80 million

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