Answer:
M = 1/0.000121 = 8264.5 years
Step-by-step explanation:
M = − k ∫∞₀ teᵏᵗdt
To obtain this mean life, we'll use integration by parts to integrate the function ∫ teᵏᵗdt
∫udv = uv - ∫ vdu
u = t
du/dt = 1
du = dt
∫ dv = ∫ eᵏᵗdt
v = eᵏᵗ/k
∫udv = ∫ teᵏᵗdt
uv = teᵏᵗ/k
∫ vdu = eᵏᵗ/k
∫ teᵏᵗdt = (teᵏᵗ/k) - ∫eᵏᵗ/k
But, ∫eᵏᵗ/k = (1/k) ∫eᵏᵗ = (1/k²) eᵏᵗ = eᵏᵗ/k²
∫ teᵏᵗdt = (teᵏᵗ/k) - eᵏᵗ/k²
The rest of the calculation is done on paper in the image attached to this question
A) the z score for 95% is 1.96
Multiply by the deviation:
1.96 x 0.005 = 0.0098
Now add and then subtract that from the mean:
4.035 - 0.0098 = 4.0252
4.035 + 0.0098 = 4.0448
The interval is (4.0252, 4.0448)
B) 4.035 +/- 1.96 x sqrt( 0.005/sqrt(25))
= 4.035 +/-0.00196
Answer: ( 4.033, 4.037)
C) the conclusion is that both 4.020 and 4.055 are out of the range.
4.020 is below the lowest range and 5.055 is higher than highest range.