Question

Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 4.7 millimeters (mm) and a standard deviation of 1.6 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

Answer Date: 02/05/2016 The data represent thickness measurements of ancient prehistoric Native American pot shards discovered in a Hop1 village are approximately normally distributed, with a mean of 4.70 millimetres (mm) and a standard deviation of1.60 mm. a) The probability thatthe thickness is less than 3.00 mm is, First, compute thez score then find probability based on standard normal table Forx 3.00 converts to 3.00 4.70 1.60 From the standard normal distribution table, the associated probability for the area to the left is shownbelow,

plz-1.06)-0.1446 The probability that the thickness is less than 3.00 mm is0.1446 b) The probability thatthe thickness is more than 7.00 mm is, First, compute the z score then find probability based on standard normal table. Forx- 7.00 converts to 7.00 4.70 1.60 From the standard normal distribution table, the associated probability is 0.9251. Since find the area to the right, so subtract from 1 to get,

P(z >1.44) 1-(Z <1.44) -1-0.9251 0.0749 The probability that the thickness is more than 7.00 mm is 0.0749 c) The probability thatthe thickness is between 3.00 and 7.00 mm is, First, compute the z score then find probability based on standard normal table Forx 3.00 converts to 3.00 4.70 1.60 Forx - 7.00 converts to

7.00 4.70 1.60 From the standard normal distribution table, the associated probability for z values and subtracts the probability is, p(3.00 s x 7.00) p(-1.06 zs1.44) p(z š 1.44) p(zs -1.06) 0.9251 0.1446 - 0.7805 The probability that the thickness is between 3.00 and 7.00 mm is 0.7805