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

=

the answer

b. they are parallel and will never intersect.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.