Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backup generators fail 41% of the times when they are needed. A hospital has two backup generators so that power is available if one of them fails during a power outage. Complete parts (a) and (b) below. a. Find the probability that both generators fail during a power outage. |(Round to four decimal places as needed.) b. Find the probability of having a working generator in the event of a power outage. Is that probability high enough for the hospital? Assume the hospital needs both generators to fail less than 1% of the time when needed. |(Round to four decimal places as needed.) Is that probability high enough for the hospital? Select the correct answer below and, if necessary, fill in the answer box to complete your choice. O A. Yes, because it is impossible for both generators to fail. B. No, because both generators fail about % of the time they are needed. Given the importance of the hospital's needs, the reliability should be improved. (Round to the nearest whole number as needed.) OC. Yes, because both generators fail about % of the time they are needed, which is low enough to not impact the health of patients. (Round to the nearest whole number as needed.)
Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backup generators fail 41% of the times when they are needed. A hospital has two backup generators so that power is available if one of them fails during a power outage. Complete parts (a) and (b) below. a. Find the probability that both generators fail during a power outage. |(Round to four decimal places as needed.) b. Find the probability of having a working generator in the event of a power outage. Is that probability high enough for the hospital? Assume the hospital needs both generators to fail less than 1% of the time when needed. |(Round to four decimal places as needed.) Is that probability high enough for the hospital? Select the correct answer below and, if necessary, fill in the answer box to complete your choice. O A. Yes, because it is impossible for both generators to fail. B. No, because both generators fail about % of the time they are needed. Given the importance of the hospital's needs, the reliability should be improved. (Round to the nearest whole number as needed.) OC. Yes, because both generators fail about % of the time they are needed, which is low enough to not impact the health of patients. (Round to the nearest whole number as needed.)
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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Question
Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backup generators fail 41% of the times when they are needed. A hospital has two backup generators so that power is available if one of them fails during a power outage. Complete parts (a) and (b) below.
Transcribed Image Text:Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that
emergency backup generators fail 41% of the times when they are needed. A hospital has two backup generators so
that power is available if one of them fails during a power outage. Complete parts (a) and (b) below.
a. Find the probability that both generators fail during a power outage.
| (Round to four decimal places as needed.)
b. Find the probability of having a working generator in the event of a power outage. Is that probability high enough for
the hospital? Assume the hospital needs both generators to fail less than 1% of the time when needed.
| (Round to four decimal places as needed.)
Is that probability high enough for the hospital? Select the correct answer below and, if necessary, fill in the answer box
to complete your choice.
O A. Yes, because it is impossible for both generators to fail.
O B. No, because both generators fail about % of the time they are needed. Given the importance of the
hospital's needs, the reliability should be improved.
(Round to the nearest whole number as needed.)
OC. Yes, because both generators fail about % of the time they are needed, which is low enough to not impact
the health of patients.
(Round to the nearest whole number as needed.)
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