Question

With its recent legalization, you are interested in how many of your classmates have tried marijuana. The government predicts that 60% of college students have used marijuana. You ask 12 12 of your classmates about their experiences. Round your answer to 4 decimals

A) what is the probability that exactly 6 have tried it?

B) what is the probability that least 10 have tried it?

C) what is the probability that less than 10 have tried it?

D) what is the probability that between 4 and 6 have tried it?

E) find the mea and standard deviation of this binomial probability distribution

Answer 1

p=0.6

1-p =0.4

n=12

Binomial distribution

P(X =x) = nCx * p^x * (1-p)^(n-x)

A)

P(X= 6) = 12C6 * 0.6^6 * 0.4^6

= 0.1766

B)

P(X >= 10) = P(X =10) + p(x=11) + p(x=12)

= 12C10 * 0.6^10 * 0.4^2 + 12C11 * 0.6^11 * 0.4^1 + 12C12 * 0.6^12 * 0.4^0

=0.0638 + 0.0174 + 0.00218

= 0.0834

C)

P(x < 10) = 1 - [p(x=10) +p(x=11)+p(x=12)]

= 1 - 0.0834

=0.9166

D)

P( 4 < x < 6) =p(4) + p(5) + p(6)

= 12C4 * 0.6^4 * 0.4^8 + 12C5 * 0.6^5 * 0.4^7 + 12C6 * 0.6^6 * 0.4^6

= 0.042 + 0.101 + 0.1766

= 0.3196

E)

Mean = np = 12*0.6 = 7.2

Standard deviation = √(np(1-p))

= √(12 *0.6*0.4)

=√2.88

= 1.697