Compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If so, approximate P(X) using the normal distribution and compare the result with the exact probability. n=60, p=0.4, x=20

And using the normal approximation we have:

And we can use the z score formula and we got:

And using the normal standard distribution table we got:

So we see that the results are very similar

Step-by-step explanation:

Let X the random variable of interest, on this case we now that:

The probability mass function for the Binomial distribution is given as:

Where (nCx) means combinatory and it's given by this formula:

And we want to find this probability:

And we can find the probability using the probability mass function

Using the normal approximation we need to find the mean and the deviation:

And using the normal approximation we have:

And we can use the z score formula and we got:

And using the normal standard distribution table we got:

So we see that the results are very similar

step-by-step explanation:

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