Please show work A machine lasts up to 10 years. The figure below shows the dens

Question

Please show work

A machine lasts up to 10 years. The figure below shows the density function, p(t), for the length of time it lasts. (a) What is the value of C ? C = (b) Is a machine more likely to break in its first year or in its tenth year? In its first or second year? The machine is The machine is (c) What fraction of the machines lasts 2 years or less? Between 5 and7 years? Between 3 and 6 years? Enter exact answers. The fraction of the machines that last 2 years or less is The fraction of the machines that last between 5 and 7 years is The fraction of the machines that last between 3 and 6 years is

Explanation / Answer

(a)

Integral (0->10) p(t)dt =1

=> (0.05 * 5 ) + 5C =1

=> 0.25 + 5C =1

=> 5C = 0.75

=> C = 0.15 Answer

(b)

i) More area is under 9–10 than under 0–1, so they are more likely to break in their 10th year.

ii) No difference here!

The same area is under 1–2 as under 0–1, so just as many break in the first year as break in the second.

(c)

i) Lasts 2 years or less

Fraction = Integral (0->2) p(t)dt = 0.05 * (2-0) = 0.1 Answer

ii) Lasts between 5 and 7 years

Fraction = Integral (5->7) p(t)dt = 0.15 * (7-5) = 0.3 Answer

iii) Lasts between 3 and 6 years

Fraction = Integral (3->6) p(t)dt = 0.05 * (5-3) + 0.15 * (6-5) = 0.25 Answer

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