Meg travels often and lately has become lax about giving herself enough time to get to the airport. She leaves home 45 minutes before the last call for her flight. Her travel time from her front door to the airport parking lot is normally distributed with a mean of 25 minutes and a standard deviation of 3 minutes. From the parking lot, she must then take a shuttle bus to the terminal and go through security. The mean time for doing this is 15 minutes and the standard deviation is 2 minutes, and this time also is normally distributed. The drive time and airport time are independent of each other. What is the probability that Meg will miss her flight because her totally time for getting to the airport is more than 45 minutes?