Question

In a statistics quiz with 10 multiple choice questions, if the probability of correctly guessing the answer to a question is 0.35. What is the probability that: a. A student correctly guesses more than 7 questions? b. What is the variance Question (c) For this Question, assume a Poisson distribution. If the average number of auto accidents that occur in a given intersection is 5 per year. What is the probability that more than 12 accidents occurs in the same intersection in the next 2years

Answer 1

muu OHC IN solution : no. of multiple choice questions (n) = 10 probability of correct guessing the answer (P) = 0,35 Let & be the number of students who guess the right answer - (a) P(x >7) ? since x is discute and binomial, having n and p, percobability of getting exactly a successes = "cz (p)* (9)*** => P(x >7) = P(x=8) + P(x=9) + P(x=10) = "(0.359(0.63) + ', (0,35) (0,05)' + 10%.(0.35)" (0.65)

Note: q= 1 p = 1-0.35 = 0.65 | - P(x>7) = 45 (0.358 (0.6572 + 10 (0.35)? (0.65)' + 1(0,35) (0.65) = 0.0048 So probability of co erect by guessing more than 7 answers = 0.0048 (6) an Variance ; for binomial if n and p are given, variance = nx px (1-P) Variance = 10 x(0.35) * (1-0.35) = 10*0.35- *0.65 7 = 2.275