A car is designed to last an average of 12 years with a standard deviation of 0.8 years.
What is the probability that a car will last less than 10 years?
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To find the probability that a car will last less than 10 years, we can use a standard normal distribution. However, we first need to transform the problem into a standard normal distribution.
To do this, we use the z-score formula: z = (x - μ) / σ, where x is the value we are interested in, μ is the mean, and σ is the standard deviation.
In this case, x = 10 years, μ = 12 years, and σ = 0.8 years.
Now we can calculate the z-score:
z = (10 - 12) / 0.8 = -2.5
Next, we need to find the cumulative probability (area under the curve) to the left of the z-score. We can look up this probability in a standard normal distribution table or use statistical software.
Using the standard normal distribution table, the probability corresponding to a z-score of -2.5 is approximately 0.0062.
Therefore, the probability that a car will last less than 10 years is approximately 0.0062 or 0.62%.