A manufacturer knows that their items have a normally distributed lifespan, with a mean of 4.1 years, and standard deviation of 1.1 years.
If you randomly purchase one item, what is the probability it will last longer than 3 years?
Given: = 4.1, = 1.1
To find the probability, we need to find the Z scores first.
For P (X > 3) = 1 - P (X < 3), as the normal tables give us the left tailed probability only.
For P( X < 3); Z = (3 – 4.1)/1.1 = -1
The probability for P(X < 3) from the normal distribution tables is = 0.1587
Therefore the required probability = 1 – 0.1587 = 0.8413
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