SOLUTION: If np &#8805; 5 and nq &#8805; 5, estimate P(fewer than 5) with n = 14 and p = 0.6 by using the normal distribution as an approximation to the binomial distribution; if np <5 or nq

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Question 1115036: If np ≥ 5 and nq ≥ 5, estimate P(fewer than 5) with n = 14 and p = 0.6 by using the normal distribution as an approximation to the binomial distribution; if np <5 or nq < 5, then state that the normal approximation is not suitable.
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
np = mean = 14 * 0.6 = 8.4
:
nq = 14 * (1-0.6) = 5.6
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Note np = 8.4 > or = 5 and nq = 5.6 > or = 5
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variance = 8.4 * (1-0.6) = 3.36
:
standard deviation = square root(3.36) = 1.833
:
z-score = (5 - 8.4) / 1.833 = -1.85
:
lookup z-score in table of z-scores to find associated probaility
:
Probability (X < 5) = 0.0322
: