The weight of male babies less than 2 months old in the United States is normally distributed with mean 12.5 pounds and standard deviation 5.1 pounds.

(a) Find the 81st percentile of the baby weights.

(b) Find the 18th percentile of the baby weights.

(c) Find the first quartile of the baby weights.

Use Excel and round the answers to at least two decimal places.

To solve these problems, we can use the properties of a normal distribution and Excel functions. Specifically, we will use the `NORM.INV` function, which returns the inverse of the normal cumulative distribution for a given probability.

The formula we use in Excel is:

```
=NORM.INV(probability, mean, standard_deviation)
```

Where:
- **probability**: The percentile value (as a decimal).
- **mean**: The average weight of the babies (12.5 pounds).
- **standard_deviation**: The standard deviation (5.1 pounds).

Now, let's find each requested percentile:

### (a) Find the 81st percentile of the baby weights.
In this case:
- Probability = 0.81
- Mean = 12.5
- Standard deviation = 5.1

Using the formula:

```
=NORM.INV(0.81, 12.5, 5.1)
```

### (b) Find the 18th percentile of the baby weights.
Here:
- Probability = 0.18
- Mean = 12.5
- Standard deviation = 5.1

Using the formula:

```
=NORM.INV(0.18, 12.5, 5.1)
```

### (c) Find the first quartile of the baby weights.
The first quartile corresponds to the 25th percentile:
- Probability = 0.25
- Mean = 12.5
- Standard deviation = 5.1

Using the formula:

```
=NORM.INV(0.25, 12.5, 5.1)
```

Using Excel, you would get the following results (rounded to two decimal places):

- **81st percentile** ≈ 17.88 pounds
- **18th percentile** ≈ 8.28 pounds
- **1st quartile (25th percentile)** ≈ 9.06 pounds

Would you like me to go into more detail or clarify any part of this process? 

Here are 5 related questions for you:

1. What is the 90th percentile for baby weights?
2. How would you interpret the result for the 81st percentile?
3. How can you use Excel to find percentiles for other distributions?
4. What is the range of baby weights for the middle 50% (interquartile range)?
5. How would a higher standard deviation affect the distribution of baby weights?

**Tip:** In Excel, the `NORM.DIST` function can be used to find cumulative probabilities given a certain weight, while `NORM.INV` is used to find the weight corresponding to a specific percentile.

The weight of male babies less than 2 months old in the United States is normally distributed with mean 12.5 pounds and standard deviation 5.1 pounds.

(a) Find the 81st percentile of the baby weights.
(b) Find the 18th percentile of the baby weights.
(c) Find the first quartile of the baby weights.

Learn how to calculate the 81st and 18th percentiles, as well as the first quartile, for a normal distribution of baby weights with a mean of 12.5 pounds and standard deviation of 5.1 pounds. Includes step-by-step instructions using Excel and the NORM.INV function.

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