p.2 STAT 200 Exam #2 hapter 6 Discrete Probability Distributions (35%) 5. The fo

Question

p.2 STAT 200 Exam #2 hapter 6 Discrete Probability Distributions (35%) 5. The following data, obtained from the Sullivan Statistics Survey, represent the number of speeding tickets individuals received in the past 12 months. Tickets x Freauency Px) 169 21 854 106 020 .020 a) Compute the mean of the random variable X. b) Compute the standard deviation of the random variable x. According to the American Lung Association, 90% of adult smokers started smoking before turning 21 years old. Use this statistic to help answer the following. 6. 10 adult smokers, use an appropriate formula to find the probability that exactly 8 of In a random sample of them started smoking before 21 years of age. a) b) In a random sample of 11 adult smokers, use an appropriate table to find the probability that between 6 and 10 adult smokers, inclusive, started smoking before 21 years of age.

Explanation / Answer

A) mean = E(x) = 0 * 0.854 + 1 * 0.106 + 2 * 0.020 + 3 * 0.020= 0.206

B) E(x2) = 0^2 * 0.0854 + 1^2 * 0.106 + 2^2 * 0.020 + 3^2 * 0.020 = 0.366

Variance = E(x2) - (E (x ))2

= 0.366 - 0.042 = 0.324

Standard deviation = sqrt(0.324) = 0.569

6)a) n = 10

P = 0.9

P(X = 8) = 10C8 * (0.9)^8 * (0.1)^2 = 0.194

B)n = 11

P = 0.9

P(6 < x < 10) = P (x = 6) + P(x = 7) + P (x = 8) + P (x = 9)

= 11C6 * (0.9)^6 * (0.1)^5 + 11C7 * (0.9)^7 * (0.1)^4 + 11C8 * (0.9)^8 * (0.1)^3 + 11C9 * (0.9)^9 * (0.1)^2 = 0.30

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