(Solved): Question 5 (25 points, Gaussian Distribution Usage): (a) (5 Pts.) x is normally distributed with ...
Question 5 (25 points, Gaussian Distribution Usage): (a) (5 Pts.)
xis normally distributed with
x∼N(c_(1),4), i.e.
\sigma ^(2)=4, determine
P(2e^(x)-4>0)(b) (5 Pts.) For the scenario in Q.2, (Medipol’s Polin Cafe distributes a coupon whenever a students buys a coffee. There are three types of coupons: ’2 free coffees’, ’1 free coffee’, and ’Buy again’ coupons. The coupons are randomly placed in a coupon box, and the cashier randomly chooses one. The probability of getting ’2 free coffee’ coupon is c1/100, while the probability of ’1 free coffee’ coupon is c4/100.) assume that have found 1000 students who purchased
c_(4)coffees. What is the probability that at least half of them got at least one free coffee coupons (either free coffee coupon)? (c) (5 Pts.) For the scenario is Part b, if we choose 100 students among the 1000 students, what is the probability that we get at least 20 students who got ' 2 free coffee coupons'? (d) (5 Pts.) Student Hasmet buys 3 coffees per day. What is the probability that he gets more than 50 '1 free coffee coupons' for one year? Take a year as 365 days. (e) (5 Pts.) Polin sells 100 coffees per hour. What is the probability that it gives away at least
10\times c_(4)either of the free coffee coupons in one day? c1=4 c4=10
