If np or equals 5 and nq or equals 5 estimate Pfewer than

If np > or equals 5 and nq > or equals 5, estimate P(fewer than 2) with n=14and p=0.4 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.

A - P(fewer than 2)_______? OR

B - The normal approximation is not suitable.

Solution

As

n p = 14*0.4 = 5.6
n q = 14*(1-0.4) = 8.4

Then a normal approximation can be used. [OPTION A]

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As

mean = n p = 5.6

standard deviation = sqrt(n p q) = sqrt(14*0.4*0.6) = 1.833030278

Then we get the left tailed area of x = 1.5. (Fewer than 2, with continuity correction.]

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    1.5      
u = mean =    5.6      
          
s = standard deviation =    1.833030278      
          
Thus,          
          
z = (x - u) / s =    -2.236733375      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -2.236733375   ) =    0.012651886

Thus,

P(fewer than 2) = 0.012651886 [ANSWER]