2.When rolling anoctahedron (8 faces) what is the expected outcome of each toss? [2]

3.Use a z-score chart to calculate P ( Z < - 0.96 ). [2]

4. When rolling an octahedron, what is the probability that the first time that you roll a 4 is on the 7^thattempt? What is the expected number of rolls before you roll a 4?[3]

5. A binomial distribution has 200 trials and a probability of success of 5%.Would a normal

approximation be viable for this situation? Show your calculations. [2]

6. A die is rolled 2 times. Let x be the number of fours that occur. Represent the probability distribution

function with a table and a graph. [4]

Communication

7.WouldP(X= 1) =P(X= 4) in a binomial distribution wheren= 5 andp= 0.5? Explain. [3]

8.Ten cards are dealt from a standard deck. The number of red cards are counted. Can this situation be modelled by a geometric distribution? Explain your reasoning. Find the probability that out of the 10 cards, 3 red cards are dealt. [3]

Application

9.Rohit is an engineer who designs roller coasters. He wants to develop a ride that 95% of the population

can ride. The average adult in NorthAmerica has a mass of 73.1 kg with a standard deviation of 14.3

kg.What range of masses should he be prepared to anticipate?

.In a manufacturing process it is estimated that 1% of the products are defective.

a) If a client places an order for 20 of the products, what is the probability that at least one of them is

defective? [3]

b) What is the expected number of defective items? [1]

12 A co-ed soccer team has 8 women and 6 men on its roster.6 players play on the field at one time.

a)What is the probability the starting lineup will have 3 men and 3 women on it? [2]

b)What is the probability the starting lineup will have at least 5 men on it? [3]

Inquiry

13.Suppose you randomly choose an integerabetween 1 and 3 (inclusive), and then draw an equilateral triangle with side length ofa cm.What is the expected area of this triangle to the nearest hundredth of a centimetre square?[5]

14. A tuna producer claims that its cans of tuna contain a standard amount of tuna.It has been

determined that of 200 cans manufactured, 92% contain the standard amount.An inspector will

only accept a shipment if at least 175 out of 200 sample cans contain more than the standard

amount.What is the probability that the shipment is accepted? [4]