Answer:
Mean = 984
Standard deviation = 13.31 (2 d.p.)
Explanation:
To find the mean and the standard deviation for the number of high school graduates in groups of 1200 Americans over the age of 25, we can model the given scenario as a binomial distribution.
Binomial distribution

where:
- X is the random variable that represents the number of successes.
- n is the fixed number of independent trials.
- p is the probability of success in each trial.
Given that 82% of Americans over the age of 25 are high school graduates, and the number of trials is 1200:
Therefore:

where the random variable X represents the number of Americans over the age of 25 who are high school graduates.
The mean (μ) for a binomial distribution is given by:

Substituting n = 1200 and p = 0.82 into the formula gives:

Therefore, the mean for the number of high school graduates in groups of 1200 Americans over the age of 25 is 984.
The standard deviation (σ) for a binomial distribution is given by:

Substituting n = 1200 and p = 0.82 into the formula gives:





Therefore, the standard deviation for the number of high school graduates in groups of 1200 Americans over the age of 25 is 13.31 (rounded to 2 decimal places).