Question

A research team at Cornell University conducted a study showing that approximately 10% of all businessmen who wear ties wear them so tightly that they actually reduce the blood flow to the brain, diminishing cerebral functions (Source: Chances: Risks and Odds in Everyday Life, by James Burke). At a board meeting, 20 businessmen wear ties.

a. Using the binomial formula, set up the probability that 12 businessmen wear ties that are tied too tightly and then simplify.

A biologist is studying a new hybrid tomato. It is known that the seeds of this hybrid tomato have probability 0.70 of germinating. The biologist plants six seeds. Define success as ‘seed germinates’.

a. What is the probability that exactly four seeds will germinate?

b. What is the probability that at least four seeds will germinate?

c. What is the probability that at most six seeds will germinate?

d. What is the probability that none will germinate?

e. What is the probability that no more than three seeds will germinate?

Answer 1

1)

2)

Given, n = 6 and p = 0.7

	P(0)	0.000729	BINOM.DIST(0,6,0.7,FALSE)
	P(1)	0.010206	BINOM.DIST(1,6,0.7,FALSE)
	P(2)	0.059535	BINOM.DIST(2,6,0.7,FALSE)
	P(3)	0.18522	BINOM.DIST(3,6,0.7,FALSE)
a	P(4)	0.324135	BINOM.DIST(4,6,0.7,FALSE)
	P(5)	0.302526	BINOM.DIST(5,6,0.7,FALSE)
	P(6)	0.117649	BINOM.DIST(6,6,0.7,FALSE)
b	P(X >= 4)	0.74431	P(4)+P(5)+P(6)
c	P(X≤6)	1	P(0)+P(1)+P(2)+P(3)+P(4)+P(5)+P(6)
d	p(0)	0.000729	BINOM.DIST(0,6,0.7,FALSE)
e	P(X≤3)	0.25569	P(0)+P(1)+P(2)+P(3)