Question

According to the Centers for Disease Control and Prevention, heart disease causes 35% of deaths in the United States. Suppose a sample of 16 recently deceased from across the U.S. were examined for cause of death.

1) Find the probability that between 6 and 11, exclusive, of the recently deceased died due to heart disease.

2) Find the probability that less than 4 of the recently deceased died due to heart disease.

Answer 1

Probability Mass Function of Binomial distribution is

Part 1)

P ( 6 < X < 11 ) = P ( X = 7 ) + P ( X = 8 ) + P ( X = 9 ) + P ( X = 10 )

P ( 6 < X < 11 ) = 0.3056

Part b)

P ( X < 4 )

P ( X < 4 ) = 0.1338