Betty’s Bite-Size Candies are packaged in bags. The number of candies per bag is normally distributed, with a mean of 50 candies and a standard deviation of 3. At a quality control checkpoint, a sample of bags is checked, and 4 bags contain fewer than 47 candies. How many bags were probably taken as samples?

Question

A. 25 bags
B. 12 bags
C. 8 bags
D. 5 bags

Answer 1

We can use the normal distribution to find the probability of a bag containing fewer than 47 candies:

$P(X<47) = P\left(Z < \frac{47 - 50}{3}\right) = P(Z < -1)$

Using a standard normal table or calculator, we find that $P(Z < -1) \approx 0.1587$.

So the probability that a randomly selected bag contains fewer than 47 candies is about 0.1587.

If we assume that the bags are sampled independently, then the number of bags containing fewer than 47 candies follows a binomial distribution with parameters $n$ (number of bags sampled) and $p=0.1587$ (probability of a bag containing fewer than 47 candies).

We want to find the value of $n$ that makes it likely to observe 4 or more bags containing fewer than 47 candies. In other words, we want to find the smallest value of $n$ such that:

$P(X \ge 4) = 1 - P(X < 4) \approx 0.05$

Using a binomial distribution table or calculator, we can find that $P(X \ge 4) \approx 0.0495$ when $n = 25$. So the answer is A. 25 bags were probably taken as samples.

Answer 2

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Answer 3

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