Find the mean mu and standard deviation omega for a binomial random variable X w

Question

Find the mean mu and standard deviation omega for a binomial random variable X with n = 300 an p = 0.75. Answer: mu = 225; omega = 7.5. Find the expected value and standard deviation for a random variable X that counts the number of fours we get when we roll a die 60 times. Would it be unusual to roll a die 60 times and get no fours at all? Answer: Expected value: 10; standard deviation 2.9; No fours would be unusual. Due to a printing error, none of the 50 multiple-choice questions on the final exam in Probability is readable, and the students taking the exam have to answer each question by randomly selecting (a), (b), (c), or (d). Under these circumstances, what is the "usual" range for the number of correct answers? Answer: 7 to 18 correct answers

Explanation / Answer

Answer:

n=50

p= probability of correct answer = ¼ =0.25

Expectation = np = 12.5

Variance = np(1 - p) = 9.375

Standard deviation = 3.06

X is usual if   µ-2 x µ+2

X is usual if   12.5-2*3.06 x 12.5-2*3.06

X is usual if   6.38 x 18.88

Approximate to whole numbers,

We get X is usual if   7 x 18

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