Question

If the distribution is really (5.43,0.54)

, what proportion of observations would be less than 5.79?
(Enter your answer rounded to four decimal places.)

Answer 1

0.7486 = 74.86% observations would be less than 5.79

Explanation:

I suppose there was a small typing mistake, so i am going to use the distribution as N (5.43,0.54)

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

The general format of the normal distribution is:

N(mean, standard deviation)

Which means that:

`\mu = 5.43, \sigma = 0.54`

What proportion of observations would be less than 5.79?

This is the pvalue of Z when X = 5.79. So

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

`Z = (5.79 - 5.43)/(0.54)`

`Z = 0.67`

`Z = 0.67` has a pvalue of 0.7486

0.7486 = 74.86% observations would be less than 5.79