Probability question

Question

The probability that you will win a game is 0.37.

a) If you play the game 1150 times, what is the most likely number of wins?

   

b) Find the standard deviation for the probability distribution.

σ =   

c) The range rule of thumb specifies that the minimum usual value for a random variable is μ–2σ and the maximum usual value is μ+2σ. You already found μ and σ from parts a and b.

Use the range rule of thumb to find the usual range of values.

Usual values = 

Answer 1

Ayobami

a) By the law of large numbers, if an experiment happens N times, when N is very large, expected successes = Np. So 1150 is a large number of experiments, so expected successes = 1150 x 0.37 = 425.5, so round to 426.

b) You have a binomial probability distribution here, as there are two possible outcomes each time.

It can be modelled approximately as a normal, with μ = Np, σ = Np (1-p)

So you can now find σ

(c) Just use your values from (a) (b) here (you found μ in part (a))

Mike