According to the Centers for Disease Control and Prevention, heart disease causes 35% of deaths in the United States. Suppose a sample of 15 recently deceased from across the U.S. were examined for cause of death. Find the probability that between 3 and 8, exclusive, of the recently deceased died due to heart disease. Find the probability that less than 4 of the recently deceased died due to heart disease.
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Given that the probability of dying due to heart disease is 0.35, we can use the binomial distribution formula to calculate this probability. \[ P(3 < x < 8) = P(x=4) + P(x=5) + P(x=6) + P(x=7) \] \[ = \binom{15}{4} \times 0.35^4 \times 0.65^{15-4} + \binom{15}{5} Show more…
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