Question

Find the upper 20%of the weight?

Answer 1

The upper 20% of the weighs are weights of at least X, which is
`X = 0.84\sigma + \mu`, in which
`\sigma` is the standard deviation of all weights and
`\mu` is the mean.

Explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the z-score of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Upper 20% of weights:

The upper 20% of the weighs are weighs of at least X, which is found when Z has a p-value of 0.8. So X when Z = 0.84. Then

`Z = (X - \mu)/(\sigma)`

`0.84 = (X - \mu)/(\sigma)`

`X = 0.84\sigma + \mu`

The upper 20% of the weighs are weights of at least X, which is
`X = 0.84\sigma + \mu`, in which
`\sigma` is the standard deviation of all weights and
`\mu` is the mean.