csat-suneung 2019 Q15

csat-suneung · South-Korea · csat__math-science 4 marks Normal Distribution Normal Distribution Combined with Total Probability or Bayes' Theorem
The commute time of employees at a certain company on a certain day follows a normal distribution with mean 66.4 minutes and standard deviation 15 minutes. Among employees whose commute time is 73 minutes or more, 40\% used the subway, and among employees whose commute time is less than 73 minutes, 20\% used the subway, with the remaining employees using other transportation. What is the probability that a randomly selected employee from those who commuted on that day used the subway? (Here, when $Z$ is a random variable following the standard normal distribution, $\mathrm { P } ( 0 \leq Z \leq 0.44 ) = 0.17$.) [4 points]
(1) 0.306
(2) 0.296
(3) 0.286
(4) 0.276
(5) 0.266
The commute time of employees at a certain company on a certain day follows a normal distribution with mean 66.4 minutes and standard deviation 15 minutes. Among employees whose commute time is 73 minutes or more, 40\% used the subway, and among employees whose commute time is less than 73 minutes, 20\% used the subway, with the remaining employees using other transportation. What is the probability that a randomly selected employee from those who commuted on that day used the subway? (Here, when $Z$ is a random variable following the standard normal distribution, $\mathrm { P } ( 0 \leq Z \leq 0.44 ) = 0.17$.) [4 points]\\
(1) 0.306\\
(2) 0.296\\
(3) 0.286\\
(4) 0.276\\
(5) 0.266