A manufacturer of matches randomly and independently puts 15 matches in each box of matches produced. The company knows that one-tenth of 6 percent of the matches are flawed. What is the probability that a matchbox will have one or fewer matches with a flaw?

a) 0.005515

b) 0.006704

c) 0.9940

d) 0.9137

e) 0.9964

f) None of the above

Question

Mathematics

Tyler Pacheco

15 February, 06:19

A manufacturer of matches randomly and independently puts 15 matches in each box of matches produced. The company knows that one-tenth of 6 percent of the matches are flawed. What is the probability that a matchbox will have one or fewer matches with a flaw?

a) 0.005515

b) 0.006704

c) 0.9940

d) 0.9137

e) 0.9964

f) None of the above

+1

Answers (1)

Know the Answer?

Spencer Benjamin · Answer 1

e) 0.9964

Step-by-step explanation:

6% = 0.06

One tenth of 6% = 0.006

X ~ B (15, 0.006)

q = 1 - 0.006 = 0.994

P (X = 0, 1)

(15C1*0.006*0.994¹⁴) + 0.994¹⁵

= 0.9964113451