For a given biased coin, the probability that the outcome of a toss is a head…
2021
For a given biased coin, the probability that the outcome of a toss is a head is 0.4. This coin is tossed 1,000 times. Let X denote the random variable whose value is the number of times that head appeared in these 1,000 tosses. The standard deviation of X (rounded to 2 decimal place) is _________ .
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Correct answer: 15 to 16
Final answer: 15.49
The random variable X follows a binomial distribution with parameters n = 1000 and p = 0.4.
Standard deviation formula: σ = sqrt(n p (1 - p)).
Compute variance: n p (1 - p) = 1000 × 0.4 × 0.6 = 240.
Standard deviation: σ = sqrt(240) ≈ 15.491933. Rounded to two decimal places: 15.49.