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GATE CSE 2021 Set 2 Q32: Standard deviation of heads in 1000 biased coin tosses

Question

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 places) is ________.

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Numerical answer. No negative marking.
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Answer: 15 to 16 (official GATE 2021 final answer key)

Concept used: X is binomial with variance np(1−p)np(1-p).

First step: Variance =1000×0.4×0.6=240= 1000 \times 0.4 \times 0.6 = 240; take the square root.

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Source: official GATE 2021 Set 2 CS question paper and final answer key, organised by IIT Bombay. Question paper · Answer key

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