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

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation:

step-by-step explanation:

idk the answer i want to say 10 but then it would be equal so try 9 but then yeah so yeah we love edgen