The distance from a customer's home to a traditional market follows a normal distribution with mean 1740 m and standard deviation 500 m. Among customers whose distance from home to market is 2000 m or more, 15\% use private vehicles to come to the market, and among customers whose distance is less than 2000 m, 5\% use private vehicles. When one customer who came to the market using a private vehicle is randomly selected, what is the probability that the distance from this customer's home to the market is less than 2000 m? (Here, when $Z$ is a random variable following the standard normal distribution, use $\mathrm { P } ( 0 \leqq Z \leqq 0.52 ) = 0.2$ for calculation.) [3 points] (1) $\frac { 3 } { 8 }$ (2) $\frac { 7 } { 16 }$ (3) $\frac { 1 } { 2 }$ (4) $\frac { 9 } { 16 }$ (5) $\frac { 5 } { 8 }$
The distance from a customer's home to a traditional market follows a normal distribution with mean 1740 m and standard deviation 500 m. Among customers whose distance from home to market is 2000 m or more, 15\% use private vehicles to come to the market, and among customers whose distance is less than 2000 m, 5\% use private vehicles. When one customer who came to the market using a private vehicle is randomly selected, what is the probability that the distance from this customer's home to the market is less than 2000 m? (Here, when $Z$ is a random variable following the standard normal distribution, use $\mathrm { P } ( 0 \leqq Z \leqq 0.52 ) = 0.2$ for calculation.) [3 points]\\
(1) $\frac { 3 } { 8 }$\\
(2) $\frac { 7 } { 16 }$\\
(3) $\frac { 1 } { 2 }$\\
(4) $\frac { 9 } { 16 }$\\
(5) $\frac { 5 } { 8 }$