Mathematics Practice Exam With Answers (5 Solved Questions)

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Question 1 7/7 pts | You may find the following files helpful throughout the exam: Statistics Equation Sheet =» Standard Normal Table =, A factory has six safety systems. During an emergency, the probability of any one of the safety systems failing is .05. What is the probability that five or more safety systems will fail during an emergency? Your Answer: For exactly 5 failures let n=6 x=5 p=0.05 [r= ptt pie Bl e0.05%(1 - 0.057°-" = 800531051 = 17me 10 For exactly 6 failures let n=6 x=6 p=0.05 [r- Tr pI -p)o- R= goes -0.05%~9=T+0.05%55)°= 16” Study.
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the probability of 5 or more failures= 1.78x10"-6 + 1.6x10"-8 = 1.796x10"-6 ‘ » For five, we have n=6, x=5, and p=05. f= —"pa-pyro = psia-osytt =178x10* "Na-a P 546-5)! hd For six, we have n=6, x=6, and pw=.05. ( Mp pro 0si1- sy 9 = 1 56x10 me Ll Tor ial te A So, the probability of five or six failing 178% 10 415610" = 1.796 x10" Study
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Question 2 12/12pts | You may find the following files helpful throughout the exam: Statistics Equation Sheet =» Standard Normal Table =» Find each of the following probabilities: a. Find P(Z < -0.87). b. Find P(Z 2 .93). c. Find P(-.59 <Z < -36). Your Answer: a) 0.19215 b|P(Z>0.93) = 1 — P(Z<0.93) =|1-0.82381- 0.17619 c) A(-0.59<Z< —0.36) = A(Z< —0.36) — P(Z< —0.59) = 0.35942 - 0.27760 = 0.08182

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