Question

Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 4.6 millimeters (mm) and a standard deviation of 1.1 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

Answer #1

Part a)

P ( X < 3 )

Standardizing the value

Z = ( 3 - 4.6 ) / 1.1

Z = -1.45

P ( X < 3 ) = P ( Z < -1.45 )

P ( X < 3 ) = 0.0735

Part b)

P ( X > 7 ) = 1 - P ( X < 7 )

Standardizing the value

Z = ( 7 - 4.6 ) / 1.1

Z = 2.18

P ( Z > 2.18 )

P ( X > 7 ) = 1 - P ( Z < 2.18 )

P ( X > 7 ) = 1 - 0.9854

P ( X > 7 ) = 0.0146

Part c)

P ( 3 < X < 7 )

Standardizing the value

Z = ( 3 - 4.6 ) / 1.1

Z = -1.45

Z = ( 7 - 4.6 ) / 1.1

Z = 2.18

P ( -1.45 < Z < 2.18 )

P ( 3 < X < 7 ) = P ( Z < 2.18 ) - P ( Z < -1.45
)

P ( 3 < X < 7 ) = 0.9854 - 0.0729

P ( 3 < X < 7 ) = 0.9125

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distributed, with a mean of 5.2 millimeters (mm) and a standard
deviation of 1.0 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

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pot shards discovered in a Hopi village are approximately normally
distributed, with a mean of 5.1 millimeters (mm) and a standard
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(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

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pot shards discovered in a Hopi village are approximately normally
distributed, with a mean of 5.5 millimeters (mm) and a standard
deviation of 1.5 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

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distributed, with a mean of 5.2 millimeters (mm) and a standard
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(a) the thickness is less than 3.0 mm
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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
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probabilities. (Round your answers to four decimal places.) (a) the
thickness is less than 3.0 mm Incorrect: Your answer is incorrect.
(b) the thickness is more than 7.0 mm (c) the thickness is between
3.0 mm and 7.0 mm

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