Potatoes - Samples: Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 8.0 ounces and a standard deviation of 1.3 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? Enter your answer as a percentage rounded to one decimal place.
_____%
X ~ N ( µ = 8 , σ = 1.3 )
P ( 7.5 < X̅ < 8.5 )
Standardizing the value
Z = ( X - µ ) / ( σ / √(n))
Z = ( 7.5 - 8 ) / ( 1.3 / √(6))
Z = -0.9421
Z = ( 8.5 - 8 ) / ( 1.3 / √(6))
Z = 0.9421
P ( -0.94 < Z < 0.94 )
P ( 7.5 < X̅ < 8.5 ) = P ( Z < 0.94 ) - P ( Z < -0.94
)
P ( 7.5 < X̅ < 8.5 ) = 0.8269 - 0.1731
P ( 7.5 < X̅ < 8.5 ) = 0.6539
Percentage = 0.6539 * 100 = 65.39%
Potatoes - Samples: Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean...
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