SOLUTION: It is known that 66% of all sown plant seeds germinates. What is the probability that after sowing 2386 seeds the germinated ones will fall in the range (1569, 1587)? That more tha

Question 1192909: It is known that 66% of all sown plant seeds germinates. What is the probability that after sowing 2386 seeds the germinated ones will fall in the range (1569, 1587)? That more than 1587 seeds will germinate? Use De Moivre - Laplace theorem
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
np=2386*0.66=1574.8 mean
variance is np(1-p)=np*0.34=535.42
sd=sqrt(V)=23.14
z=(x-mean)/sd, where the lower value is 1568.5 and the upper value is 1587.5
lower value is z=6.3/23.14=-0.27 and upper value is z=12.7/23.14=0.55
probability of z in that range is 0.3153. The last digit depends upon where one rounds z.
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>1587 is z>0.55 using 1587.5 again as the bottom value (not 1587). That probability is 0.2912
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