A research team conducted a study showing that approximately 20% of all businessmen who wear ties wear them so tightly that they actually reduce blood flow to the brain, diminishing cerebral functions. At a board meeting of 15 businessmen, all of whom wear ties, what are the following probabilities? at least one tie is too tight?
more than two ties are too tight?
no tie is too tight?
at least 13 ties are not too tight?

1. 0.9648

2. 0.602

3. 0.0352

4. 0.398

Step-by-step explanation:

We solve using binomial probability

n = 15

P = 20% = 0.2

1. At least 1 is tight

= P(X>=1)

P(X>=1) = 1-p(X= 0)

= P(x=0)

= 15C0(0.20)⁰(1-0.20)^15-0

= 15C0(0.20)⁰(80)¹⁵

= 0.0352

P(x>=1) = 1-0.0352

= 0.9648

2.

More than 2 ties tight

P(X>2)

P(X>2) = 1-p(X<=2)

p(X<=2) = p(x=0) + p(x=1) + p(x=2)

= p(x=0) = 0.0352

p(x=1) = 15C1(0.20)¹(0.80)¹⁴

= 0.1314

p(x=2) = 15C2(0.20)²(0.80)¹³

= 0.2309

P(x>2) = 1-(0.0352+0.1314+0.2309)

= 0.602

3.

No ties is tight

P(X = 0)

= 15C0(0.20)⁰(0.80)¹⁵

= 0.0352

4.

At least 3 are not tight

This says that at most we have 3 to be too tight

= p(X<=2) = p(x=0) + p(x=1) + p(x=2)

= 0.0352+0.1319+0.2309

= 0.398

answer: the dogs need to shift their focus to human scent.

its because the dogs being trained are for search and rescue thus they need to be able to track humans and their specific scent

d

gimmee one of those gold crowns!

~coco