Question

The number of potato chips in a bag is normally distributed with a mean of 71 and a standard deviation of 2. Approximately what percent of bags contain between 69 and 73 potato chips?

Approximately 68%
Approximately 71%
Approximately 95%
Approximately 99.7%

Answer 1

Approximately 68% percent of bags contain between 69 and 73 potato chips.

Explanation:

Number of chips in a bag is normally distributed.

Mean = 71

Standard deviation = 2

We know that in normal distribution, 34.1% of bags will fall with in one standard deviation on one side. On both sides within the range of 1 standard deviation, 34.1 + 34.1 = 68.2 % of bags will fall.

A table of normal distribution about mean is attached for better understanding.

Our range is:

69 to 73

71 - 2 to 71 + 2

71 ± 2

mean ± standard deviation

Our range is within 1 standard deviation. Hence, Approximately 68% of bags contain between 69 and 73 potato chips.

Answer 2

Approximately 68%

Explanation:

The number of potato chips in a bag is normally distributed with a mean of 71 and a standard deviation of 2, that is to say:

X ∼ N(µ, σ2) ⇒ X ∼ N(71, 4).

Now, to find the percentage of bags that contain between 69 and 73 potatos we need the help of a calculator.

Pluging the data into a calculator we get that the percentage of bags that contain between 69 and 73 potatos is 68.27% ≈ 68%.

The solution is: Approximately 68%