Approximately 10% of all people are left-handed ("11 little-known facts,"2013). Consider a grouping of fifteen people.

Question

a.State the random variable.

b.) Argue that this is a binomial experiment.

Find the probability that

c.) None are left-handed.

d.) Seven are left-handed.

e.) At least two are left-handed.

f.) At most three are left-handed.

g.) At least seven are left-handed.

h.) Seven of the last 15 U.S. Presidents were left-handed. Is this unusual? What does that tell you?

Answer 1

a) a typical example of a random variable is the outcome of a coin toss, either heads or tails

same with randomly selecting people where the outcome is whether they are right or left handed

the Expected outcome = np = 15(.1) = 1 1/2 Lefthanded people when randomly selected from 15 people.

variance = npq = 15(.1).9) = 1.5(.9) = 1.35

standard deviation = sqr1.35 = about 1.16

b) it's a classic binomial, similar to flipping an unfair coin that comes up tails 10% of the time and heads 90% of the time. Just two outcomes. (this ignores bidextrous people, like President James A. Garfield who could write left and right handed or coins that land on their edge or roll away with no known outcome)

c) None are Left handed. 15 randomly selected. 10% Lefthanded

Pr(L=0) = .9^15

d) Pr(L=7) = 15C7(.9)^8(.1)^7

e) Pr(L>1) = 1 - P(L=0) - P(L=1)= 1- (.9)^15 - 15(.9)^14(.1)

f) Pr(L<4) = P(0) +P(1) + P(2) + P(3) = .9^15 + 15(.9^14)(.1) + 15C2(.9^13)(.1)^2 + 15C3(.9^12)(.1)^2

g) Pr(L>6) = 1 - P(0)+P(1)+P(2)+P(3)+P(4)+P(5)

once you calculate f) above, P(L<4) then P(L>6) =1- P(L<4)- P(L=4) -P(L+5) + P(L=6)

h) in a) the standard deviation = 1.13 and mean = 1.5

(7-1.5)/1.13 = 5.5/1.13 = z score about 5 which is very unusual,

but that assumes a normal distribution, while the binomial is highly skewed

calculate d) above and it tells you how exceptional 7 out of 15 left handed presidents is

it's very unusual, but within the realm of possibility due to mere chance

if there's more than chance at work, maybe it's due to how left handed people face obstacles more than right handed people do, and try harder to overcome them, including their trying to becoming presidential candidates

nCr = n!/r!(n-r)!

for example

15C2 = 15!/2!13! = 15x14/2 =15x7

15C1 = 15!/1!14! = 15

P(L=x) = nCx(.9)^(15-x)(.1)^x

P(L=0) = 15C0(.9)^15(1) = .9^15

presidents counted as left handed are 8

Garfield

Hoover

Truman

Ford

Reagan

George HW Bush

Clinton

Obama

2 others had left hand abilities

Jefferson & Wilson

both originally right handed but switched well after injuries to their right hand

10 out of 46 is higher than 10% or sometimes 13% considered lefties in the general population

10 of 46 = about 22%

Julius Caesar, Benjamin Netanyahu and many other world leaders throughout history have also been Left handed

Babe Ruth was left handed. Being left handed is a distict advantage to batters as they're closer to 1st base from the batter's box. In major league baseball, about 25% of pitchers have been left handed,

Architechs and lawyers have the most left handers among professions. Mathematicians, orthopedic surgeons and librarians the least. Helen Keller and Lewis Carroll were left handed.

The right left brain psychology or neurobiology may be at work, as the left half of the brain controls the right side of the body and vice versa.

August 13 is international left handed day

Is there any correlation between left handed people and left wing politics?

5 south paw Republican Presidents 3 south paw Democrat presidents

No corrleation between left handedness and IQ

only 45% of left handed people are also left footed

95% of right handed people are also right footed

something like 47% of right handed people are right eyed

56% of left handed people are left eyed.

No left footed international day or left eyed day either

How many left footed presidents has the US had?

apparently in the 19th century baseball diamonds were laid out in a westerly direction, so that the left handed pitcher's throwing arm was on the south side of the park, so they were called "southpaws"

are criminals more likely to be more disproportionately left handed? Jack the Ripper was left handed. Serial killers tend to be more left handed. See the movie "Lincoln Lawyer"

any connection between being in left field or sinister if left handed?

identical twins more often are both the same handedness, both right or both left handed, but not always. some identical twins are one lefty and one righty. There is a genetic factor. Yet George HW Bush was left handed while son George W Bush was right handed.

King George VI and Queen Victoria were lefties. So was Prince William, but none of his children were left handed.