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In: Statistics and Probability

If np greater than or equals 5 and nq greater than or equals​ 5, estimate Upper...

If np greater than or equals 5 and nq greater than or equals​ 5, estimate Upper P left parenthesis at least 8 right parenthesis with n equals 13 and p equals 0.6 by using the normal distribution as an approximation to the binomial​ distribution; if np less than 5 or nq less than ​5, then state that the normal approximation is not suitable. P(at least 8) =?

Solutions

Expert Solution

Let X be the number of successes in n trials. X has a Binomial distribution with parameters, number of trials n=13 and the success probability, p=0.6

Now the test for np and nq

ans: np greater than or equals 5 and nq greater than or equals​ 5 and hence we can use normal approximation to binomial distribution.

First we get the following

The expected value of X is (using the formula for the Binomial expectation)

The standard deviation of X is (using the formula for the Binomial distribution)

We can say that X has approximately a normal distribution with mean and standard deviation

The probability that X is at least 8 (which is 8 or more) is

ans: P(at least 8) = 0.5675 (using the normal approximation)

orchestra answered 2 years ago
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