Question

Use the normal approximation to find the indicated probability.

Answer 1

The indicated probability is 0.07548.

When can we use the normal approximation to the binomial distribution?

The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with , as long as .

$E(X) = np\\\\Var(X) = np(1-p)$

we have that:

n = 84, p = 0.4: P(X> 26)

np = 84 x 0.4 = 33.6

n(1 - p) = 84 x 0.6 = 50.4 .

we can use the online binomial probability distribution calculator :

P(X≥ 26 ) = 0.07548

Hence the indicated probability is 0.07548.

More can be learned about the normal approximation to the binomial distribution at;

brainly.com/question/14424710

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