The basic input/output system (BIOS)is a chip every computer has. When you rst turn your computer on, before your operating system loads, your computer uses

The “basic input/output system” (BIOS)is a chip every computer has. When you first turn your computer on, before your operating system loads, your computer uses the BIOS to take care of e.g., keyboard input, output to the screen, and reading files from your hard drive. If your BIOS chip fails, your computer cannot boot up. The lifetime X (in hours) of a BIOS chip on a computer has a Weibull distribution with α = 2.5 and β = 5000.

(a) Calculate the mean and standard deviation of X.

(b) Calculate the probability that a BIOS chip lasts more than 5000 hours.