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ivanzaharov [21]
3 years ago
7

What, roughly, is the percent uncertainty in the volume of a spherical beach ball whose radius is r = 2.86 plus or minus .09 m?

Mathematics
1 answer:
Aleksandr-060686 [28]3 years ago
3 0
The volume of a sphere is calculated through the equation,
  
       V = 4πr³ /3
where r is the radius of the given. 

If the radius is 2.86, we can substitute the value to the equation above such that,
         V = 4π(2.86)³ / 3 = 97.99π m³

When the radius is 0.09 m plus the given radius then,
       V = 4π(2.86 - 0.09)³ / 3 = 89.03π m³

The difference between the volumes is equal to,
       difference = 97.99π - 89.03π m³ = 8.96π m³

Dividing this to the original volume and multiplying by 100%,
    percentage = (8.96π/97.99π) x 100% 
    percentage = 9.14%.

Hence, the expected percent uncertainty is equal to 9.14%. 
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The probability that a normally distributed data with a mean, μ and standard deviation, σ is greater than a given value, a is given by:

P(x\ \textgreater \ a)=1-P(x\ \textless \ a)=1-P\left(z\ \textless \  \frac{a-\mu}{\sigma}\right)

Given that the average precipitation in Toledo, Ohio for the past 7 months is 19.32 inches with a standard deviation of 2.44 inches, the probability that <span>a randomly selected year will have precipitation greater than 18 inches for the first 7 months is given by:

P(x\ \textgreater \ 18)=1-P(x\ \textless \ 18) \\  \\ =1-P\left(z\ \textless \ \frac{18-19.32}{2.44}\right) \\  \\ =1-P(z\ \textless \ -0.5410) \\  \\ =1-0.29426=\bold{0.7057}



Part B:

</span>The probability that an n randomly selected samples of a normally distributed data with a mean, μ and standard deviation, σ is greater than a given value, a is given by:

P(x\ \textgreater \ a)=1-P(x\ \textless \ a)=1-P\left(z\ \textless \ \frac{a-\mu}{\frac{\sigma}{\sqrt{n}}}\right)

Given that the average precipitation in Toledo, Ohio for the past 7 months is 19.32 inches with a standard deviation of 2.44 inches, the probability that <span>5 randomly selected years will have precipitation greater than 18 inches for the first 7 months is given by:

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