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Fittoniya [83]
3 years ago
9

Suppose the weights of farmer carl's potatoes are normally distributed with a mean of 8.0 ounces and a standard deviation of 1.1

ounces. suppose carl bags his potatoes in randomly selected groups of 6. what percentage of these bags should have a mean potato weight between 7.5 and 8.5 ounces?
Mathematics
1 answer:
denis23 [38]3 years ago
6 0
Given that <span>the weights of farmer carl's potatoes are normally distributed with a mean of 8.0 ounces and a standard deviation of 1.1 ounces.

The probability of a normally distributed data between two values (a, b) is given by:

P(a\ \textless \  X\ \textless \  b)=P\left(z\ \textless \  \frac{b-\mu}{\sigma/\sqrt{n}} \right)-P\left(z\ \textless \  \frac{a-\mu}{\sigma/\sqrt{n}} \right) \\  \\ =P(7.5\ \textless \ X\ \textless \ 8.5)=P\left(z\ \textless \  \frac{8.5-8.0}{1.1/\sqrt{6}} \right)-P\left(z\ \textless \  \frac{7.5-8.0}{1.1/\sqrt{6}} \right) \\  \\ =P(z\ \textless \ 1.113)-P(-1.113)=0.8672-0.1328=0.7344</span>
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