If the mean value of the weight of a particular brand of dog food bag is 20.6 pounds and the standard deviation is 1.3, assume a normal distribution and calculate the percentage of bags that falls below the lower specification value of 19.7 pounds.

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To calculate the percentage of bags that falls below the lower specification value of 19.7 pounds, we can use the z-score formula and the standard normal distribution.

First, we need to calculate the z-score for the lower specification value using the formula:

z = (X - μ) / σ

where:
X = lower specification value (19.7 pounds)
μ = mean (20.6 pounds)
σ = standard deviation (1.3)

Plugging in the values, we get:

z = (19.7 - 20.6) / 1.3 = -0.69

Next, we need to find the percentage of values below this z-score using the standard normal distribution table or a calculator. The z-score represents the number of standard deviations away from the mean.

Looking up the z-score of -0.69 in the standard normal distribution table, we find that the area to the left of this z-score is approximately 0.2431.

To convert this value to a percentage, we multiply by 100:

0.2431 * 100 = 24.31%

Therefore, approximately 24.31% of bags will fall below the lower specification of 19.7 pounds.