Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 4.9 millimeters (mm) and a standard deviation of 1.4 mm. For a randomly found shard, find the following probabilities. (Round your answers to four decimal places.) (a) the thickness is less than 3.0 mm .087 Correct: Your answer is correct. (b) the thickness is more than 7.0 mm

a) 0.0869 = 8.69% probability that the thickness is less than 3.0 mm

b) 0.0668 = 6.68% probability that the thickness is more than 7.0 mm

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:

(a) the thickness is less than 3.0 mm

This is the pvalue of Z when X = 3.

has a pvalue of 0.0869

0.0869 = 8.69% probability that the thickness is less than 3.0 mm

(b) the thickness is more than 7.0 mm

This is 1 subtracted by the pvalue of Z when X = 7. So

has a pvalue of 0.9332

1 - 0.9332 = 0.0668

0.0668 = 6.68% probability that the thickness is more than 7.0 mm

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step-by-step explanation: