Question

Asked Dec 3, 2019

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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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