In a bag of 390 chocolate​ candies..

Question

In a bag of 390 chocolate​ candies, 41 of them are brown. The candy company claims that 13​% of its plain chocolate candies are brown. For the​ following, assume that the claim of 13​% is​ true, and assume that a sample consists of 390 chocolate candies. Complete parts​ (a) through​ (e) below.

a. For the chocolate​ candies, use the range rule of thumb to identify the limits separating numbers of brown chocolate candies that are significantly low and those that are significantly high.

Answer 1

Amanda,

Disclaimer: The Range Rule of Thumb is typically not applied in this case, so I'm giving you my best guess.

I believe your teacher/professor is testing some understanding and the other parts b-e will probably yield more reasonable results. But, let's continue and try to apply this here.

The range rule is typically applied to numerical data and as a rule of thumb it's:

σ ≈ range / 4

In your case, the range of possible numbers the brown candies could be is: [0, 390] (none or all of them). This means our estimated standard deviation is:

σ ≈ 390 / 4 ≈ 97.5

Typically we consider things outside of [μ - 2σ, μ + 2σ] suspicious. Remember, for normal within 2σ gives us 95% of the data.

Applying that here with the assumption that 13% is the true proportion we get:

[0.13 * 390 - 2 * 97.5, 0.13 * 390 + 2 * 97.5] = [-144.3, 245.7]

But, negative candies is impossible so let's clip it and do a little rounding:

[0, 246] so only significantly high exists of [247, 390]

Meaning we'd only contend the 13% claim if we got over 246 brown candies.

These could be the separating numbers we get if we only use the rule of thumb. This is not a super appropriate model here and I'm sure that parts b-e use much better models for this like: Normal approximation of Binomial distribution.