Question

(The Normal Approximation to the Binomial Distribution) You toss a fair coin 150 times, and count the number of heads X. We know X has a binomial distribution with mean 75 and standard deviation approximately 6.12 (you should be able to verify this!). Use a binomial distribution to find the probability that the coin lands heads 80 or more times. Now, given a random variable that has a normal distribution with mean 75 and standard deviation 6.12, find the probability it takes on a value of 80 or greater. Given a random variable that has a normal distribution with mean 75 and standard deviation 6.12, find the probability it takes on a value of 79.5 or greater. Note that the first and last result above agree closely. This technique is called the "normal approximation to the binomial". In the last part, 79.5 is said to be the "continuity corrected" version of the point we are interested in

          (The Normal Approximation to the Binomial Distribution)

You toss a fair coin 150 times, and count the number of heads X. We know X has a binomial distribution with mean 75 and standard deviation approximately 6.12 (you should be able to verify this!).

Use a binomial distribution to find the probability that the coin lands heads 80 or more times.

Now, given a random variable that has a normal distribution with mean 75 and standard deviation 6.12, find the probability it takes on a value of 80 or greater.

Given a random variable that has a normal distribution with mean 75 and standard deviation 6.12, find the probability it takes on a value of 79.5 or greater.

Note that the first and last result above agree closely. This technique is called the "normal approximation to the binomial". In the last part, 79.5 is said to be the "continuity corrected" version of the point we are interested in

(The Normal Approximation to the Binomial Distribution)

You toss a fair coin 150 times, and count the number of heads X. We know X has a binomial distribution with mean 75 and standard deviation approximately 6.12 (you should be able to verify this!).

Use a binomial distribution to find the probability that the coin lands heads 80 or more times.

Now, given a random variable that has a normal distribution with mean 75 and standard deviation 6.12, find the probability it takes on a value of 80 or greater.

Given a random variable that has a normal distribution with mean 75 and standard deviation 6.12, find the probability it takes on a value of 79.5 or greater.

Note that the first and last result above agree closely. This technique is called the "normal approximation to the binomial". In the last part, 79.5 is said to be the "continuity corrected" version of the point we are interested in

Added by Thomas W.

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