Thickness measurement ancient prehistoric Native American Pot Shards discovered in Hopi Village are approximately normally distributed with the mean of 5.1 millimeters and standard deviation of 0.9 millimeters. For a randomly found shard, What is the probability that the thickness is: a) Less than 3.0 millimeters b) More than 7.0 millimeters Present your answer in three decimal places. Present your answer for "a",answer for "b" Group of answer choices

a)

And we can find this probability using the normal standard table and we got:

b)

And we can find this probability using the complement rule and the  normal standard table and we got:

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

Where and

Part a

We are interested on this probability

And the best way to solve this problem is using the normal standard distribution and the z score given by:

If we apply this formula to our probability we got this:

And we can find this probability using the normal standard table and we got:

Part b

We are interested on this probability

And the best way to solve this problem is using the normal standard distribution and the z score given by:

If we apply this formula to our probability we got this:

And we can find this probability using the complement rule and the  normal standard table and we got:

step-by-step explanation:

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