Question

Using the Normal Approximation (50pts)

1. Suppose you play 1000 spins of Roulette and on each time you bet that the ball will land on a red number.

a. what is the distribution of X: the number of reds you get in 1000 spins of the wheel? (5-pt).

b. On average how many reds do you expect to get in 1000 spins of the wheel? (i.e. what is μx ?) (5-pt)

c. What is the standard deviation for the number of reds in 1000 spins of the wheel? (i.e. what is σx ?) (5-pt)

d. What is the normal distribution that best approximates the number of reds give 1000 spins? (5-pts)

2. Use the normal approximation to compute the z-score corresponding to winning:

a. 470 times (2-pt)

b. 495times (2-pt)

c. 460times (2-pt)

d. 480 times(2-pt)

e. 450 times(2-pt)

3. Use the normal approximation to compute the probability of winning

a. More than 470 times: P(X > 470)? (5-pts)

b. P (X<475)? (5-pts)

c. P(X>500)? (5-pts) i. Note winning more than 500 times is necessary to walk away a ‘winner’ if you bet the same amount each time.

d. P(X<500)? (5pts) i. Note winning less than 500 times means you walk away a ‘loser’ if you bet the same amount each time.

Answer 1

Answer: