# If no 25 and nq 25, estimate P(fewer than 7) with n 14rseapproximation is not suitable.andp 0.6 by using the normal distribution as an approximation to the binomial distribution; if np< 5 or nq

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Step 1

The binomial distribution can be approximated to normal if np is greater than 5 and nq is also greater than 5.

Here,

Both np and nq are greater than 5. Thus, the normal distribution as an approximation of binomial can be used.

The mean and standard deviation of the normal distribution are,

Step 2

Before calculating the probability, the continuity correction factor is applied. Since, the discrete distribution is approximated to a continuous distribution, a continuity correction factor is used to compute the probability.

That is, P(X<7-0.5) =P(X<6.5)

The probability of getting fewer than 7 successes is calculated below:

Step 3

The probability value corresponding to the Z-sco...

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