Answer:
Now we can use the z score formula in order to find the X value who satisfy the condition:
Explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:
Where
and
And the best way to solve this problem is using the normal standard distribution and the z score given by:
We can begin finding a value on the z table who accumulate 0.99 of the area on the left and 0.01 on the right and this value is:
Now we can use the z score formula in order to find the X value who satisfy the condition:
And we know that the value needs to have 1lb under the surchage weight so the final answer for this case would be: