The time required for a citizen to complete the 2010 U. S. Census "long" form is normally distributed with a mean of 40 minutes and a standard deviation of 10 minutes. The lowest 10 percent of the citizens would need at least how many minutes to complete the form

The lowest 10 percent of the citizens would need at least 52.8 minutes to complete the form.

Step-by-step explanation:

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

In a set with mean and standard deviation , the zscore of a measure X is given by:

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.

In this problem, we have that:

The slowest 10 percent of the citizens would need at least how many minutes to complete the form

This is the value of X when Z has a pvalue of 0.9. So it is X when Z = 1.28.

The lowest 10 percent of the citizens would need at least 52.8 minutes to complete the form.

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step-by-step explanation: