SOLUTION: If np ≥ 5 and nq ≥ 5, estimate P(more than 9) with n =14 and p=0.7 by using the normal distribution as an approximation to the binomial distribution; if np< 5 or nq<5,
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Question 899622: If np ≥ 5 and nq ≥ 5, estimate P(more than 9) with n =14 and p=0.7 by using the normal distribution as an approximation to the binomial distribution; if np< 5 or nq<5, then state the normal approximation is not suitable.
P (more than 9) =
Round to four decimal places as needed
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
n = 14
p = 0.7
np = 14*0.7 = 9.8
So np = 9.8 and np > 5
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n = 14
q = 1-p = 1-0.7 = 0.3
q = 0.3
nq = 14*0.3 = 4.2
nq = 4.2
nq > 5 is NOT true. Also nq is not equal to 5 either.
nq < 5 which means that the normal approximation is not suitable
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You can use the binomial distribution formula (for pdf) and then add up the values from x = 10 to x = 14
However, a much quicker way is to use a calculator like this one: http://stattrek.com/online-calculator/binomial.aspx
and we get the answer
P(X > 9) = 0.5842 (this is approximate)
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