A machine packages bags of almonds. The weights of the bags are normally distributed with a mean of 14 oz and a standard deviation of 1.2 oz.
Enter the z-score of a bag of almonds that weighs 12.2 oz.
my answer: -1.5
looks good
To find the z-score for a given value, we use the formula:
z = (x - μ) / σ
where:
- z is the z-score
- x is the given value
- μ is the mean of the distribution
- σ is the standard deviation of the distribution
In this case, the mean (μ) is 14 oz and the standard deviation (σ) is 1.2 oz. We want to find the z-score for a bag of almonds that weighs 12.2 oz.
Plugging the values into the formula:
z = (12.2 - 14) / 1.2
z = -1.8 / 1.2
z = -1.5
Therefore, the z-score of a bag of almonds weighing 12.2 oz is -1.5.
To find the z-score, you can use the formula:
z = (x - μ) / σ
where x is the observed value, μ is the mean, and σ is the standard deviation.
In this case:
x = 12.2 oz
μ = 14 oz
σ = 1.2 oz
Plugging the values into the formula:
z = (12.2 - 14) / 1.2
z = (-1.8) / 1.2
z = -1.5
So the z-score of a bag of almonds weighing 12.2 oz is -1.5.