222k views
5 votes
The weights of oranges are normally distributed with a mean of 12.4 pounds and a standard deviation of 3 pounds. Find the minimum weight that would be included in the top 5

1 Answer

5 votes

Final answer:

To find the minimum weight included in the top 5% of the distribution, use the z-score formula and a z-table or calculator to find the corresponding z-value. Then, rearrange the z-score formula to solve for the minimum weight.

Step-by-step explanation:

To find the minimum weight that would be included in the top 5%, we need to find the z-score that corresponds to the top 5% of the normal distribution. The z-score represents the number of standard deviations a particular value is from the mean. We can use the z-score formula:

z = (x - mean) / standard deviation

To find the z-score for the top 5%, we look up the corresponding z-value in the z-table or use a calculator. In this case, the z-value for the top 5% is approximately 1.645.

Now, we can solve for the minimum weight by rearranging the z-score formula:

x = mean + (z * standard deviation)

Plugging in the values, we have:

x = 12.4 + (1.645 * 3) ≈ 17.935

Therefore, the minimum weight that would be included in the top 5% is approximately 17.935 pounds.

User Justin Drury
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories