Question

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?

Answer 1

Given that 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 \ (b-\mu)/(\sigma/√(n)) \right)-P\left(z\ \textless \ (a-\mu)/(\sigma/√(n)) \right) \\ \\ =P(7.5\ \textless \ X\ \textless \ 8.5)=P\left(z\ \textless \ (8.5-8.0)/(1.1/√(6)) \right)-P\left(z\ \textless \ (7.5-8.0)/(1.1/√(6)) \right) \\ \\ =P(z\ \textless \ 1.113)-P(-1.113)=0.8672-0.1328=0.7344`