For every 100 births in the U.S., the number of boys follows, approxiamately, a normal curve with a mean of 51 and standard deviation of 5 boys. If the next 100 births in your local hospital resulted in 36 boys (and thus 64 girls) would that be unusual?

No

To determine if the number of boys, 36, out of 100 births in your local hospital is unusual, we can use the concept of standard deviation. Here's how you can calculate and determine if it is unusual:

1. Calculate the standard deviation:
- The mean number of boys per 100 births is given as 51.
- The standard deviation is given as 5.

To calculate the standard deviation for a proportion, you need to find the square root of the product of p(1-p)/n, where p is the proportion (mean/100) and n is the number of total births (100).

In this case:
- p = 51/100 = 0.51
- n = 100

Standard deviation (SD) = √((p(1-p))/n)
SD = √((0.51(1-0.51))/100) ≈ 0.05

2. Calculate the z-score:
The z-score measures how many standard deviations a value is away from the mean. It can be calculated by subtracting the mean and dividing by the standard deviation.

In this case:
- Value = 36 (number of boys)
- Mean = 51
- Standard deviation = 0.05

Z-score = (Value - Mean) / Standard Deviation
Z-score = (36 - 51) / 0.05 ≈ -300

3. Interpret the z-score:
A z-score of -300 indicates that the number of boys in your local hospital (36) is -300 standard deviations away from the mean. Since the z-score is extremely low, it suggests that this outcome is highly unusual.

Therefore, based on the given information, it would be considered unusual to have only 36 boys out of 100 births in your local hospital.