Gtwenty percent of drivers driving between 11 pm and 3 am are drunken drivers. using the binomial probability formula, find the probability that in a random sample of 12 drivers driving between ll pm and 3 am, two to four will be drunken drivers. (round to 4 digits, ex. 0.1234)

p(2 lesser than or equal to x lesser than or equal to 4) = 0.6526

Step-by-step explanation:

20% of drivers driving between 11 PM and 3 AM are drunken drivers.

We want to use the binomial distribution to determine the probability that in a random sample of 12 drivers driving between 11 PM and 3 AM, two to four will be drunken drivers.

The formula for binomial distribution is

P( x = r) = nCr × q^n-r × p^r

x = number of drivers

p = probability that the drivers that are drunken.

q= 1-p = probability that the drivers are not drunken.

n = number of sampled drivers.

From the information given,

p = 20/100 = 0.2

q = 1 - p = 1 - 0.2 = 0.8

n = 12

We want to determine

p(2 lesser than or equal to x lesser than or equal to 4)

It is equal to p(x=2) + p(x= 3) + p(x=4)

p(x=2) = 12C2 × 0.8^10 × 0.2^2 = 0.2835

p(x=3) = 12C3 × 0.8^9 × 0.2^3 = 0.2362

p(x=4) = 12C4 × 0.8^8 × 0.2^4 = 0.1329

p(2 lesser than or equal to x lesser than or equal to 4) = 0.2835 + 0.2362 + 0.1329 = 0.6526

answer: a.   one is a factor of every whole number since every number is divisible by itself.