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?

47 = 50 - 3 or:
47 = Mean - 1 Standard deviation
For normal distribution it means that 4 bags represent 16 % of all samples.
4 bags ------ 16%
x bags ------ 100 %
---------------------------
4 * 100 = x * 16
16 x = 400
x = 400 : 16
x = 25
Answer: 25 bags were probably taken as samples.

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ajinems ajinems · Answer 2 · 2022-05-11T12:22:37+02:00

The number of bags that are probably taken as samples is = 25 bags.

What is normal distribution?

A normal distribution usually appears like a bell shape in a graph whereby the mean is centrally placed.

In the normal distribution of candies per bag;

The standard deviation =3

The mean = 50

Therefore candies per bag = 47 - 53

Using the empirical method, the percentage to the right of the line of normal distribution can be calculated as:

50 + 64/2 = 84%.

That means that 100 - 84 = 16% of the data is below 4.

If 16% = 4

100% =X

Make X the subject of formula,

X = 100× 4/16

X = 400/16

X= 25 bags.

Therefore, the number of bags that are probably taken as samples is = 25 bags.

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