Answer all questions. Please provide sufficient explanation to each question

1. The average service speed in the check-in queue of hotel is 0.2 customer per minute. If you are now in the third position of the waiting line, please find the probability of finishing the check-in procedure for you within 5 minutes. (10%) 2. A basketball player makes 90% of her free throws. What is the probability she will miss for the first time on the seventh shot? (10%) 3. In a certain city, the daily consumption of electric power (in millions of kilowatt hours) is a random - xe -/ for x > 0 variable having the probability density function, f(x) = . If the city's power plant has for x 0 ; Exponential distribution: x! for x > 0, B > 0 P(x; 3 )= P , (Supposed e=2.7183) O elsewhere