Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 4.9millimeters (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.)

Question

(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

the z-score of a sample is the number of standard deviations its thickness is from the mean thickness

calculate the z-scores , then use a z-score table to find the probabilities

Answer 2

a) Find the z-score that corresponds to a thickness of 3.0 mm:
z = (x - μ)/σ
z = (3.0 - 4.9)/1.5
z ~ -1.27
So the probability that x < 3.0, or P(X<3.0) is the same as the probability that z < -1.27.
Consult a z-score table for this probability: find -1.2 in the left column and 0.07 in the top row. These intersect at 0.10204, or ~10.2%.
b) Use the same process, except this time the probability will be 1 - P(X<7.0).
c) This time, the probability will be P(X<7.0) - P(X<3.0). Should be quick as you found these numbers in parts a) and b).

Answer 3

The 5.3 millimeters and standard deviation of 1.5 mm, the thickness of less tan 3.0 _——— .

Answer 4

Assume that x has normal distribution with the specified mean and standard deviation. Find the indicated probability ? u=112;o=16. P(x_> 90) =?

Answer 5

The answer for "A" is -2.3333 because you subtract 3.0-5.1 which equals -2.1 and then divide it by 0.9 which equals -2.3333