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Answer:
a) 0.6915; b) 2.83 years
Step-by-step explanation:
For part a,
The formula for a z score is
Our mean, μ, is 3.25 and our standard deviation, σ, is 0.5.
This gives us
z = (3-3.25)/0.5 = -0.25/0.5 = -0.5
Using a z table, we see that the area under the curve to the left of this is 0.3085. However we want the area to the right; this means we subtract from 1:
1-0.3085 = 0.6915
For part b,
We look in the cells of a z table to find the value closest to 20%, or 0.2000. This is 0.2005, which corresponds with a z score of -0.84:
-0.84 = (X-3.25)/0.5
Multiply both sides by 0.5:
0.5(-0.84) = ((X-3.25)/0.5)(0.5)
-0.42 = X-3.25
Add 3.25 to each side:
-0.42+3.25 = X-3.25+3.25
X = 2.83
The advertised life would be 2.83 years.