Forty-three percent of US teens have heard of a fax machine. You randomly select 12 US...

Forty-three percent of US teens have heard of a fax machine. You randomly select 12 US teens. Find the probability that the number of these selected teens that have heard of a fax machine is exactly six (first answer listed below). Find the probability that the number is more than 8 (second answer listed below).

Solutions

Expert Solution

The random variable X denotes number of students that have heard of a fax machine.

p = probability of a students have heard of a fax machine. = 0.43

n = number of students randomly selected = 12

X takes value 0, 1, ..,12.

The probability distribution of a random variable X is binomial with n = 12 and p = 0.43

The probability mass function of X is

P( Exactly 6 students have heard of a fax machine ) = P (X =6)

P( Exactly 6 students have heard of a fax machine ) = 0.2003.

P ( More than 8 students have heard of a fax machine ) = P (X >8)

= P( X=9) + P(X =10) + P(X=11) + P(X=12).

P ( More than 8 students have heard of a fax machine )

= 0.0205 + 0.0046 + 0.0006 + 0.00003

= 0.02573

P ( More than 8 students have heard of a fax machine ) = 0.02573.

orchestra answered 1 year ago

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