If the mean value of the weight of a particular brand of dog food is 20.6 lb and the standard deviation is 1.3, assume a normal distribution and calculate the amount of product that falls below the lower specification value of 19.7 lb
you can play around with Z table stuff at
http://davidmlane.com/hyperstat/z_table.html
To calculate the amount of product that falls below the lower specification value of 19.7 lb, we need to use the concept of z-scores.
The z-score measures the number of standard deviations a given data point is from the mean. It allows us to standardize the data and compare values across different distributions. In this case, we can use the z-score to determine the proportion of data that falls below a particular value.
The formula to calculate the z-score is:
z = (x - μ) / σ
Where:
- z is the z-score
- x is the value we want to calculate the proportion for (in this case, the lower specification value of 19.7 lb)
- μ is the mean value of the distribution (20.6 lb in this case)
- σ is the standard deviation of the distribution (1.3 lb in this case)
Now, let's plug in the values into the formula and calculate the z-score:
z = (19.7 - 20.6) / 1.3
z = -0.9 / 1.3
z ≈ -0.6923
By looking up the z-table or using statistical software, we can find the proportion of data below the z-score of -0.6923. The table or software will give us the cumulative probability, which represents the proportion of data below a given z-score.
From the z-table or software, we find that the cumulative probability for a z-score of -0.6923 is approximately 0.2451.
Therefore, approximately 24.51% of the product falls below the lower specification value of 19.7 lb.