A company wishes to make 1 ounce candy bars. According to government regulations, in order to label the candy bars as 1 ounce, at least 95 % of the bars must weigh 1 ounce or more. Our process standard deviation is .08 ounces. What do we need to make the mean weight be so that 95% weigh 1 ounce or more?

Question

A company wishes to make 1 ounce candy bars. According to government regulations, in order to label the candy bars as 1 ounce, at least 95 % of the bars must weigh 1 ounce or more. Our process standard deviation is .08 ounces. What do we need to make the mean weight be so that 95% weigh 1 ounce or more?

Answer 1

To determine the mean weight of the candy bars so that at least 95% weigh 1 ounce or more, we need to find the value that corresponds to the 95th percentile of a normal distribution.

Here's how we can calculate it step by step:

Step 1: Determine the critical value
Since we want to calculate the 95th percentile, we need to find the corresponding critical value from the standard normal distribution (Z-distribution). This value will represent the number of standard deviations from the mean.

Step 2: Find the critical value
The critical value for a one-tailed test at the 95% confidence level can be obtained using a standard normal distribution table or a calculator. Looking up the critical value will give you the Z-score.

Step 3: Calculate the mean weight
To calculate the mean weight, we need to use the formula:

Mean = Target weight + (Z-score * Standard deviation)

In this case, the target weight is 1 ounce, and the standard deviation is 0.08 ounces (as given in the question).

Substituting these values into the formula will give you the mean weight required.

Let's calculate it:

Step 1: Determine the critical value
Since the 95% confidence level requires an area of 0.95 in the right tail, the critical value can be found by subtracting 0.95 from 1:
Critical value = 1 - 0.95 = 0.05

Step 2: Find the critical value
Looking up the critical value of 0.05 in the standard normal distribution table (or using a calculator) gives you a Z-score of approximately 1.645.

Step 3: Calculate the mean weight
Using the formula mentioned earlier:

Mean = 1 + (1.645 * 0.08)
Mean = 1 + 0.1316
Mean ≈ 1.1316 ounces

Therefore, to ensure that at least 95% of the candy bars weigh 1 ounce or more, the mean weight of the candy bars should be approximately 1.1316 ounces.