Assume that 13% of people are left-handed. if we select 10 people at random, answer the following questions:

a. what is the probability that there are exactly 3 lefties in the group? . (use 3 decimal places.)

b. what is the probability that there are at least 3 lefties in the group? . (use 3 decimal places.)

c. find the expected number of right-handers in the group.

d. find the standard deviation of the number of right-handers in the group. (use 3 decimal places.)

e. what is the probability that they are not all right-handed? . (use 3 decimal places.)

f. what is the probability that there are exactly 5 righties and 5 lefties? . (use 4 decimal places.)

g. what is the probability that the majority is right-handed?

0.099, 0.969,0.87,8.3.1.063

Step-by-step explanation:

Let X be the left handed people in the sample of 10 people selected.

X is binomial with n=10 and p = 0.13

a)  the probability that there are exactly 3 lefties in the group

=

b) the probability that there are at least 3 lefties in the group

=

Now Y number of right handers is binomial with n =10 and p = 0.87

c) the expected number of right-handers in the group.

d) the standard deviation of the number of right-handers in the group

=

step-by-step explanation:

there is a formula i can give you:

it is r^2*n*sin(360/n) divided by 2 where r represents the "radius" and n is the number of sides.

plug them in:

(10sqrt(3))^2*6*sin(360/6) divided by 2

100*3*6*sin(60) divided by 2

900*sin(60)

900*sqrt(3)/2

450*sqrt(3)

approx is 779.4 cm^2