a manufacturer knows that their items have a normally distributed lifespan, with a mean of 3.1 years, and standard deviation of 0.5 years. the 10% of items with the shortest lifespan will last less than how many years? give your answer to one decimal place.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

First, we must utilize the conventional normal table to determine the value for z if 10% of the region (probability) to its left will be present. We can observe that about z = -1.282.

Now, we have to find the value of x, that corresponds to the value of z.

Since,

(x - μ) / σ = z

(x - 3.1) / 0.5 = -1.282

x = 2.459

Hence, the shortest lifespan will last less than 2.5 years.

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