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Chapter 4: Q103E (page 263)

Blood diamonds. According to Global Research News (March 4, 2014), one-fourth of all rough diamonds produced in the world are blood diamonds, i.e., diamonds mined to finance war or an insurgency. (See Exercise 3.81, p. 200.) In a random sample of 700 rough diamonds 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 = 200.

d. Find the approximate probability that the number of the 700 rough diamonds that are blood diamonds is less than or equal to 200.

Short Answer

Expert verified

a.渭=175b.蟽=11.4567c.z=2.1822d.Theapproximateprobabilityis0.9854

Step by step solution

01

Given information

According to Global Research News (March 4,2014), one-fourth of all rough diamonds produced in the world are blooddiamonds.

The blood diamond x be a binomial distribution with n = 700 and p = 0.25

02

Calculation of mean

a.渭=np=700脳14=700脳0.25=175渭=175

Thus, the mean=175.

03

Calculation of standard deviation

b.蟽=np(1-p)=700脳0.25脳(1-0.25)=11.4564蟽=11.4564

Therefore, the variance of x is 11.4564.

04

Calculation of z-score

c.渭=175蟽=11.4564x=200

The z-score is,

z=x-渭蟽=200-17511.4564=2.1822z=2.1822

Therefore, the z-score is 2.1822.

05

Finding the approximate probability

d.P(x鈮�200)=P(x鈮�200)=P(z鈮�2.1822)=0.9853713鈮�0.9854P(x鈮�200)=0.9854

Therefore, the approximate probability is 0.9854.

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