Lesson 10.2

μ (mean)= npWhere n = number of trials, p = probability of

success

σ2 (variance) = npq where q = probability of failure

σ ( standard deviation) =

Suppose a dart player has probability p of hitting the bull’s-eye with a single dart, and all attempts are independent. Prove that the expected number of bull’s eyes the player will hit in two attempts is 2p.

Binomial distribution:

0q2 + 2pq + 2p2

0 1q2

1 2pq

2 1p2

2p(q+p)2p

In the binomial distribution of tossing a far coin 250 times and counting the number of heads, what is the mean and standard deviation?

Mean: np 250 * .5 = 125 Sd: (npq).5

(250 * .5 * .5).5

7.91

For some binomial probability distribution, μ = 45 and σ = 6, find n and p.

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