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Find z z such that the proportion of observations that are less than z z in a standard normal distribution is 0.29 . 0.29. (Enter your answer rounded to two decimal places.)z= __.

User VGO
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1 Answer

3 votes

Answer:

z = -0.55.

Explanation:

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.

Find z z such that the proportion of observations that are less than z z in a standard normal distribution is 0.29 .

This is the value of Z that has a pvalue of 0.29.

So it is z = -0.55.

User Do Thanh Tung
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