(7-6)/0.65 = 1.538 std
so, look that up in your Z table to see how much lies in the right tail.
so, look that up in your Z table to see how much lies in the right tail.
Z-score formula: (x - μ) / σ
Where:
x = the value we want to find the percentage for (7)
μ = mean (6)
σ = standard deviation (0.65)
Calculating the z-score:
Z = (7 - 6) / 0.65
Z = 1.54 (rounded to two decimal places)
Now, we can use the z-score to find the corresponding percentage using a standard normal distribution table (or a calculator).
Looking up the z-score of 1.54 in the table, we find that the percentage is approximately 93.32%.
Therefore, approximately 93.32% of the milk containers will spoil in greater than 7 days after the date stamped.
To do this, we will use the z-score formula:
z = (x - μ) / σ
where:
- x is the value we want to find the percentage for (in this case, 7),
- μ is the mean of the distribution (6 days), and
- σ is the standard deviation of the distribution (0.65 days).
First, let's calculate the z-score:
z = (7 - 6) / 0.65 = 1.54
Now, we need to find the cumulative probability to the right of z = 1.54. Since the distribution is normal, we can use a standard normal distribution table or a calculator to find this probability.
Looking up the z-score of 1.54 in the standard normal distribution table, I found that the area to the left of z = 1.54 is approximately 0.9382. Therefore, the area to the right of z = 1.54 is 1 - 0.9382 = 0.0618.
So, approximately 0.0618 (or 6.18%) of the milk containers will spoil in greater than 7 days after the date stamped.