The Centers for Disease Control and Prevention reported that 25% of baby boys 6-8 months old i the United States weigh more than 20 pounds. A sample of 16 babies is studied.

Question

What is the probability that more than 6 weigh more than 20 pounds?

Answer 1

Since we have multiple trials that are either more than 20 pounds or not. Then, this could be modeled as a binomial distribution with rate p = 0.25 and total number of trials n = 16. The probability that more than 6 weight more than 20 is equal to

Pr(X > 6) = 1 - P(X <= 6) = 1 - (B(n,p,0) + B(n,p,1) + B(n,p,2) +B(n,p,3) +B(n,p,4) +B(n,p,5) +B(n,p,6) )

=1 - ( 0.01 + 0.0535 + 0.1336 + 0.2079 + 0.2252 + 0.1802 + 0.1101 )

= 0.0796