Q1) Consider random variable x=time required for college student to complete standardized exam. Assume that for population of students at school, distribution of x is well approximated by normal curve with mean 48 min and standard deviation 4 min.

a)If this exam permits 55 mins, what proportion of students at this school would be not capable to finish exam in the allotted time?

b) How much time is needed for fastest 2% of all students to complete exam?

Q2) On Blue Rabbit Slope, probability that new skier will required to be carried to the First Aid Station is 0.25. When there are new skiers in group of 40 and if we let X be number of new skiers needing to be driven to First Adis Station, find out the mean and standard deviation of X?

b) On Red Fox Slope, probability that new skier will require to be performed to the First Aid Station is 0.2. When there are new skiers in a group of 30 and if we let Y be number of new skiers needing to be driven to First Aids Station, find out the mean and standard deviation of Y?

c) Let Z be number of injuries from both slopes, find out mean and standard deviation of Z using answers of (a) and (b).

d) When 40 skiers are sent down from top of Blue Rabbit Slope, they are sent one at time. Find out the probability that first one needing to be driven to First Aid Station is the 5th one to be sent down the slope?