Question

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 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 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

Answer 1

Solution :

Given that ,

mean = = 5.4

standard deviation = = 1.0

(a)

P(x < 3.0) = P[(x - ) / < (3.0 - 5.4) / 1.0]

= P(z < -2.4)

= 0.0082

Probability = 0.0082

(b)

P(x > 7.0) = 1 - P(x < 7.0)

= 1 - P[(x - ) / < (7.0 - 5.4) / 1.0]

= 1 - P(z < 1.6)

= 1 - 0.9452

= 0.0548

Probability = 0.0548

(c)

P(3.0 < x < 7.0) = P[(3.0 - 5.4)/ 1.0) < (x - ) /  < (7.0 - 5.4) / 1.0) ]

= P(-2.4 < z < 1.6)

= P(z < 1.6) - P(z < -2.4)

= 0.9452 - 0.0082

= 0.9370

Probability = 0.9370

Thank You.