Question

In: Statistics and Probability

Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately...

Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 5.4 millimeters (mm) and a standard deviation of 0.8 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 (b) the thickness is more than 7.0 mm (c) the thickness is between 3.0 mm and 7.0 mm

Solutions

Expert Solution

Solution :

Given that,

mean = = 5.4

standard deviation = = 0.8

a ) P( x < 3.0 )

P ( x - / ) < ( 3.0 - 5.4 / 0.8)

P ( z < - 2.4 / 0.8 )

P ( z < - 3 )

Using z table

= 0.0013

Probability = 0.0013

b ) P( x > 7.0 )

= 1 -P( x < 7.0 )

= 1 -P ( x - / ) < ( 7.0 - 5.4 / 0.8)

= 1 -P ( z < 2.4 / 0.8 )

= 1 -P ( z < 3 )

Using z table

= 1 - 0.9987

= 0.0013

Probability = 0.0013

c ) P( 3.0 < x < 7.0 )

P ( 3.0 - 5.4 / 0.8) <( x - / ) < ( 7.0 - 5.4 / 0.8)

P (- 2.4 / 0.8 < z <  2.4 / 0.8 )

P (- 3 < z < 3 )

P ( z < 3 ) - P ( z < - 3 )

Using z table

= 0.9987 - 0.0013

= 0.9974

Probability = 0.9974


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