Question

A distance of 200 ft must be taped in a manner to ensure a standard deviation smaller than ± 0.04 ft. What must be the standard deviation per 100 ft tape length to achieve the desired precision?Express your answer to three significant figures and include appropriate units.

Answer 1

Answer:

The error in tapping is ±0.02828 ft.

Explanation:

Given that,

Distance = 200 ft

Standard deviation = ±0.04 ft

Length = 100 ft

We need to calculate the number of observation

Using formula of number of observation

$n=\dfrac{\text{total distance}}{\text{deviation per tape length}}$

Put the value into the formula

$n=\dfrac{200}{100}$

$n=2$

We need to calculate the error in tapping

Using formula of error

$E_{series}=\pm E\sqrt{n}$

$E=\dfrac{E_{series}}{\sqrt{n}}$

Put the value into the formula

$E=\dfrac{0.04}{\sqrt{2}}$

$E=\pm 0.02828\ ft$

Hence, The error in tapping is ±0.02828 ft.

Answer 2

Standard deviation is equal to the square root of varience.The total number of observation is 2.

 

Given that,  

Distance = 200 ft  

Standard deviation = ±0.04 ft  

Length = 100 ft

The number of observation can be calculated by,

$\bold {n= \dfrac {distance }{deviation}}$

So,

Using formula of number of observation,  

$\bold {n = \dfrac {200}{100}}\\\\\bold {n = 2 }$

Therefore, the total number of observation is 2.

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