If this procedure is repeated 100 times, what is the probability that the number of times that the coin lands tails will be less than 40

1.79% probability that the number of times that the coin lands tails will be less than 40

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

The standard deviation of the binomial distribution is:

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that , .

Fair coin:

Equally as likely to be heads or tails, so

100 times

Then

What is the probability that the number of times that the coin lands tails will be less than 40

Using continuity correction, this is , which is the pvalue of Z when X = 39.5.

has a pvalue of 0.0179

1.79% probability that the number of times that the coin lands tails will be less than 40

answer: approximately 206 bones

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