SOLUTION: If np &#8805; 5 and nq &#8805; 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,

Algebra ->  Probability-and-statistics -> SOLUTION: If np &#8805; 5 and nq &#8805; 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,      Log On


   

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) About Me  (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)