According to the Centers for Disease Control and Prevention, heart disease cause

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. Find the probability that between 7 and 12, 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. One state lottery has 1, 100 prizes of exist1, 110 prizes of exist10, 20 prizes of exist65, 5 prizes of exist335. 2 prizes of exist1, 230, and 1 prize of exist2, 700. Assume that 28,000 lottery tickets are issued and sold for exist1.

Explanation / Answer

p = 0.35

n = 16

P(X = x) = 16Cx * 0.35x * (1 - 0.35)16-x

a) P(7 < X < 12) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11)

= 16C8 * 0.358 * 0.658 + 16C9 * 0.359 * 0.657 + 16C10 * 0.3510 * 0.656 + 16C11 * 0.3511 * 0.655

= 0.0923 + 0.0442 + 0.0167 + 0.0049

= 0.1581

b) P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= 16C0 * 0.350 * 0.6516 + 16C1 * 0.351 * 0.6515 + 16C2 * 0.352 * 0.6514 + 16C3 * 0.353 * 0.6513

= 0.0451

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