The diameter of holes drilled into flat-pack furniture is normally distributed with a mean of 5mm and a standard deviation of 0.15mm. If a single item of furniture has 50 holes in it, how many have a diameter of more than 5.2mm (to the nearest whole number)?

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Quizplus · Accepted Answer

To find the number of holes with a diameter of more than 5.2mm, we first calculate the z-score for 5.2mm using the formula $z = \frac{(X - \mu)}{\sigma}$, where $X$ is the value in question (5.2mm), $\mu$ is the mean (5mm), and $\sigma$ is the standard deviation (0.15mm). This gives us $z = \frac{(5.2 - 5)}{0.15} = \frac{0.2}{0.15} = 1.33$. Looking up 1.33 on the standard normal distribution table gives us an area of approximately 0.9082 to the left of 5.2mm, meaning there's about 9.18% (1 - 0.9082) of the distribution to the right. For 50 holes, 9.18% of 50 is approximately 4.59, which rounds to 5 holes when considering the nearest whole number.

The Diameter of Holes Drilled into Flat-Pack Furniture Is Normally