$51.$ Speedy Lube The time required for Speedy Lube to complete an oil change service on an automobile approximately follows a normal distribution, with a mean of $17$ minutes and a standard deviation of $2\mathrm{.}5$ minutes. $($a$)$ Speedy Lube guarantees customers that the service will take no longer than $20$ minutes. If it does take longer, the customer will receive the service for half$-$price. What percent of customers receive the service for half price? $($b$)$ If Speedy Lube does not want to give the discount to more than $3\%$ of its customers, how long should it make the guaranteed time limit$?51.$ Speedy Lube The time required for Speedy Lube to complete an oil change service on an automobile approximately follows a normal distribution, with a mean of $17$ minutes and a standard deviation of $2\mathrm{.}5$ minutes. $($a$)$ Speedy Lube guarantees customers that the service will take no longer than $20$ minutes. If it does take longer, the customer will receive the service for half$-$price. What percent of customers receive the service for half price? $($b$)$ If Speedy Lube does not want to give the discount to more than $3\%$ of its customers, how long should it make the guaranteed time limit$?51.$ Speedy Lube The time required for Speedy Lube to complete an oil change service on an automobile approximately follows a normal distribution, with a mean of $17$ minutes and a standard deviation of $2\mathrm{.}5$ minutes. $($a$)$ Speedy Lube guarantees customers that the service will take no longer than $20$ minutes. If it does take longer, the customer will receive the service for half$-$price. What percent of customers receive the service for half price? $($b$)$ If Speedy Lube does not want to give the discount to more than $3\%$ of its customers, how long should it make the guaranteed time limit$?51.$ Speedy Lube The time required for Speedy Lube to complete an oil change service on an automobile approximately follows a normal distribution, with a mean of $17$ minutes and a standard deviation of $2\mathrm{.}5$ minutes. $($a$)$ Speedy Lube guarantees customers that the service will take no longer than $20$ minutes. If it does take longer, the customer will receive the service for half$-$price. What percent of customers receive the service for half price? $($b$)$ If Speedy Lube does not want to give the discount to more than $3\%$ of its customers, how long should it make the guaranteed time limit$?$