Assuming that the weights of newborn babies are normally distributed with mean 6.5 pounds and standard deviation 1.2 pounds, how many babies in a group of 80 do we expect to weigh more than 8.9 pounds?

Please show work
Thank you

Use processes similar to your later post.

To find the number of babies in a group of 80 that we expect to weigh more than 8.9 pounds, we need to calculate the area under the normal distribution curve to the right of 8.9 pounds.

1. Standardize the value:
First, we need to convert the value of 8.9 pounds to a standardized score (also known as a z-score) using the formula:
z = (x - μ) / σ
where x is the value, μ is the mean, and σ is the standard deviation.
In this case, x = 8.9 pounds, μ = 6.5 pounds, and σ = 1.2 pounds.
Plugging in the values:
z = (8.9 - 6.5) / 1.2
z = 2.4 / 1.2
z = 2

2. Find the area to the right of the z-score:
We then need to find the area under the standard normal distribution curve to the right of a z-score of 2. This is the probability that a randomly selected baby will weigh more than 8.9 pounds.
You can use a z-table or a calculator with a built-in function to find this probability.
If using a z-table, find the value closest to 2 in the table. The corresponding value represents the area to the left of the z-score. Since we want the area to the right, subtract this value from 1. The result represents the area to the right of the z-score.
Alternatively, you can use a calculator with a built-in function (e.g., using the cummulative probability function) to directly find the area.

Let's assume the area to the right of the z-score of 2 is approximately 0.0228.

3. Calculate the expected number of babies:
Finally, we can calculate the expected number of babies in the group of 80 who weigh more than 8.9 pounds by multiplying the probability by the total number of babies in the group:
Expected number = probability * total number of babies
Expected number = 0.0228 * 80
Expected number ≈ 1.82

Therefore, we expect approximately 1.82 babies in the group of 80 to weigh more than 8.9 pounds. Since we cannot have a fraction of a baby, we can say that we would expect either 1 or 2 babies to weigh more than 8.9 pounds.