The number of cigarettes smoked per day by adults forms a normal distribution. The average number of cigarettes smoked per day is 20 with a standard deviation of 7. What number of cigarettes would represent the 35th percentile?

17.3 cigarettes represent the 35th percentile

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:

What number of cigarettes would represent the 35th percentile?

This is the value of X when Z has a pvalue of 0.35. So it is X when Z = -0.385.

So

17.3 cigarettes represent the 35th percentile

56

step-by-step explanation:

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step-by-step explanation: