The probability that a transmission will last less than 14 years is 5%
Step-by-step explanation:
Given
Mean = 16 years
SD = 1.2 years
We have to find the probability that a transmission will last less than 14 years
First of all we have to find the z-score of the value
Z-score is given by:
[tex]z = \frac{Value-mean}{SD}\\= \frac{14-16}{1.2}\\= \frac{-2}{1.2}\\= -1.6666[/tex]
We will use the z-score table to find the probability of being less than 14
So,
From z-score table we get the value for -1.6666
P(z = -1.666) = 0.04846
= 0.04846* 100
= 4.846
Rounding off to nearest percentage
5%
Hence,
The probability that a transmission will last less than 14 years is 5%
Keywords: Probability, z-score
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