An unbiased die is tossed 500 times. The standard deviation of getting sixes in these 500 tosses is

An unbiased die is tossed 500 times. The standard deviation of getting sixes in these 500 tosses is
  1. $\frac{625}{9}$
  2. $\sqrt{\frac{250}{3}}$
  3. $\frac{25}{3}$
  4. $\frac{250}{3}$

Solution

$\mathrm{n}=500, \mathrm{P}=\frac{1}{6}, \mathrm{q}=\frac{5}{6}$ S.D. $=\sqrt{\mathrm{npq}}=\sqrt{500 \times \frac{1}{6} \times \frac{5}{6}}=\sqrt{\frac{2500}{36}}=\frac{50}{6}=\frac{25}{3}$

Asked in: MHT CET 2022 (06 Aug Shift 1)

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