Question

about 2% of all rough diamonds produced in a certain region are blood diamonds, that is, diamonds mined to finance war or an insurgency. in a random sample of 750 rough diamonds from this region purchased by a diamond buyer, let x be the number that are blood diamonds. a. find the mean of x. b. find the standard deviation of x. c. find the z - score for the value x = 12. d. find the approximate probability that the number of 750 rough diamonds in the region that are blood diamonds is less than or equal to 12. a. the mean is 15.00. (round to two decimal places as needed.) b. the standard deviation is 3.83. (round to two decimal places as needed.) c. the z - score is (round to two decimal places as needed.)

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value from the data set, $\mu$ is the mean, and $\sigma$ is the standard deviation.
We are given that $\mu = 15.00$, $\sigma=3.83$, and $x = 12$.

Step2: Substitute values into formula

$z=\frac{12 - 15.00}{3.83}=\frac{- 3.00}{3.83}\approx - 0.78$

Answer:

a. The mean is 15.00
b. The standard deviation is 3.83
c. The z - score is - 0.78
d. To find the probability that $x\leq12$, we look up the z - score of - 0.78 in the standard normal distribution table. The probability corresponding to $z=-0.78$ is approximately 0.2177.