2 companies, A and B, package and market a chemical substance and claim .15 of t

Question

2 companies, A and B, package and market a chemical substance and claim .15 of the total weight of the substance is sodium. However, a careful survey of 4,000 packages (half from each company) indicates the proportion varies around .15, with the results shown here:

Chemical Brand <.100 .100-.149 .150-.199 >.200
A 25% 10% 10% 5%
B 5% 5% 10% 30%

Find the percentage of all packages that had a sodium total weight proportion between .100 and .199

What is the probability that a package, randomly selected from this group, is both from company A and has a sodium total wieght proportion between .150 and .199 (Decimal, round 2 digits)

Given that a randomly selected package came from company A, what is the probability that the package has a sodium total weight proportion between .150 and .199 (decimal rounded to 2 digits)

Explanation / Answer

(a) Percentage of all packages that had a sodium total weight proportion between .100 and .199

P(.100-.149)+P(.150-.199) from both brands.

P=(10%+5%)+(10%+10%)=35%

(b) Probability that a package, randomly selected from this group, is both from company A and has a sodium total weight proportion between .150 and .199

Assuming that this question is a continuation of previous part

Total probability=0.35(35%)

P(package from company A and sodium poportion between .150 and .199)=0.10(10%)

Required probability =0.10/0.35=0.29

(c)Given that package is selected from company A.Need to find probability that the package has a sodium total weight proportion between .150 and .199

Probability that a package came from comapny A=0.5(50% are from company A)

In company A ,probability of packages having a sodium total weight proportion between .150 and .199=0.10(10%)

Required probability=(0.1/0.5)=0.20

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