## Related questions with answers

At fast-food restaurants, the lids for drink cups are made with a small amount of flexibility, so they can be stretched across the mouth of the cup and then snugly secured. When lids are too small or too large, customers can get frustrated, especially if they end up spilling their drinks. At one restaurant, large drink cups require lids with a diameter of between 3.95 and 4.05 inches. The restaurant's lid supplier claims that the diameter of the large lids follows a normal distribution with mean 3.98 inches and standard deviation 0.02 inches. Assume that the supplier's claim is true.

What percent of large lids have diameters between 3.95 and 4.05 inches?

Solution

VerifiedThis is the third part of a four-part exercise, in which we are observing a normal distribution (diameters of large lids for cups, in inches ) with mean $\mu=3.98$ inches and standard deviation $\sigma=0.02$ inches

Thus far, we computed the proportions of lids with diameters smaller than $3.95$ and greater than $4.05$ inches to be $6.68\%$ and $0.02\%$, respectively.

We want to find the proportion (percentage) of large lids with diameters between $3.95$ and $4.05$ inches.

*What is the total area below a density curve?*

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