A scientist is weighing each of 30 fishes. Their mean weight worked out is 30 gm and standard deviation of 2 gm. Later, it was found that the measuring scale was misaligned and always under reported every fish weight by 2 gm. The correct mean and standard deviation (in gm) of fishes are respectively.

# A scientist is weighing each of $30$ fishes. Their mean weight worked out is  and standard deviation of  Later, it was found that the measuring scale was misaligned and always under reported every fish weight by  The correct mean and standard deviation (in gm) of fishes are respectively.

1. A

2. B

3. C

4. D

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### Solution:

Let ${x}_{1},{x}_{2},\dots ,{x}_{30}$ be actual weights of $30$ fishes and ${y}_{1},{y}_{2},\dots ,{y}_{30}$ be the weights of fishes taken from misaligned increasing scale. Then,

$⇒\overline{\overline{)Y}}=\overline{\overline{)X}}+2$ and ${\sigma }_{Y}={\sigma }_{X}$

and ${\sigma }_{Y}=2$

and ${\sigma }_{Y}=2$

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