The actual weights of bag of pet food are normally distributed.The mean of the weights is 50.0 lb,with a standard deviation of 0.2 lb.

B) In a group of 250 bags,how many would you expect to weigh more than 50.4 lb?

To find how many bags would be expected to weigh more than 50.4 lb, we need to calculate the proportion of bags that weigh more than 50.4 lb and then multiply it by the total number of bags in the group.

Step 1: Calculate the z-score
The z-score formula is given by:
z = (x - μ) / σ

Where:
- x is the value we want to find the proportion for (50.4 lb),
- μ is the mean weight (50.0 lb),
- σ is the standard deviation (0.2 lb).

Plugging in the values:
z = (50.4 - 50.0) / 0.2
z = 0.4 / 0.2
z = 2

Step 2: Find the proportion
Using a standard normal distribution table or calculator, we can find the proportion of values above z = 2.

Looking up the proportion corresponding to z = 2, we find that it is approximately 0.0228.

Step 3: Multiply the proportion by the total number of bags
We multiply the proportion (0.0228) by the total number of bags in the group (250) to find the expected number of bags that weigh more than 50.4 lb.

Expected number = 0.0228 * 250
Expected number ≈ 5.7

Therefore, we would expect approximately 5 or 6 bags to weigh more than 50.4 lb.

To find the number of bags that would be expected to weigh more than 50.4 lb, we need to use the information given about the normal distribution of the weights.

We know that the mean weight is 50.0 lb and the standard deviation is 0.2 lb. This means that the distribution of weights follows a normal distribution curve.

To find the number of bags that would weigh more than 50.4 lb, we need to find the area under the normal curve to the right of 50.4 lb.

To do this, we can standardize the data by calculating the z-score using the formula:

z = (x - mean) / standard deviation

In this case:

z = (50.4 - 50.0) / 0.2
z = 0.4 / 0.2
z = 2

We now need to find the probability associated with a z-score of 2. We can look up this probability in a standard normal distribution table or use a calculator.

Looking up the probability in the table, we find that the probability associated with a z-score of 2 is approximately 0.9772.

This means that approximately 97.72% of the bags will weigh less than or equal to 50.4 lb. Therefore, the number of bags that would be expected to weigh more than 50.4 lb can be calculated as:

Expected number = Total number of bags * (1 - Probability)

Expected number = 250 * (1 - 0.9772)
Expected number = 250 * 0.0228
Expected number ≈ 5.7

Therefore, we would expect approximately 5.7 bags in a group of 250 bags to weigh more than 50.4 lb.

That would be 2 sigma or more above the mean.

2.5% is 2 sigma or more above the mean
2.5% is 2 sigma or more below the mean
95% is between the 2 sigma points (49.6 to 50.4 in this case)
It's something worth remembering