Answer: Our required probability would be 0.9641.
Step-by-step explanation:
Since we have given that
Number of hours he works a day = 8
So, Number of minutes he worked in a day =
Number of calls = 220
So, Average
Standard deviation
Mean = μ = 2.0 minutes
Standard deviation = σ = 1.5 minutes
Using the normal distribution, we get that
So, the probability that Albert will meet or exceed his quota would be
Hence, our required probability would be 0.9641.
Answer:
a) Y(x) = {900, x≤30; 900-40(x-30), x>30}
b) T(x) = {900x, x≤30; 2100x-40x², x>30}
c) dT/dx = {900, x≤30; 2100-80x, x>30}
Step-by-step explanation:
a) The problem statement gives the function for x ≤ 30, and gives an example of evaluating the function for x = 35. So, replacing 35 in the example with x gives the function definition for x > 30.
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b) The yield per acre is the product of the number of trees and the yield per tree:
T(x) = x·Y(x)
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c) The derivative is ...
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The attached graph shows the yield per acre (purple, overlaid by red for x<30), the total yield (black), and the derivative of the total yield (red). You will note the discontinuity in the derivative at x=30, where adding one more tree per acre suddenly makes the rate of change of yield be negative.
