It is estimated that 20 percent of all school children in America are lefthanded. Let us assume that this estimate is reasonably accurate. Consider a random sample of 12 school children taken from the population. 

(a) Compute the probability that fewer than 3 children in the sample will be lefthanded. 

P(X<3)=P(X≤2)=(Carry 4 decimal digits.) 

(b) Compute the probability that between 6 and 9 children (inclusive) will be lefthanded. 

P(6≤X≤9)=P(X≤9)-P(X≤5)=(Carry 4 decimal digits.) 

(c) Compute the probability that more than 5 children will be righthanded. 

P(X≤6)=(Carry 4 decimal digits.) 

Note: For (c) above, "more than 5 righthanded" means "less than or equal to 6 lefthanded."