IQ score are normally distributed with a mean of 95 and a standard deviation of 17. If the sample size is n=36 find the mean and standard distribution of sample mean
IQ scores are normally distributed with a mean of 95
and a standard deviation of 16
.
Assume that many samples of size n are taken from a large population of people and the mean IQ score is computed for each sample. If the sample size is n equals
36
,
find the mean and standard deviation of the distribution of sample means.
To find the mean and standard deviation of the sample mean, we can use the formulas:
Mean of sample mean (μₙ) = Mean of the population (μ)
Standard deviation of sample mean (σₙ) = Standard deviation of the population (σ) / √(Sample size)
Given:
Mean of the population (μ) = 95
Standard deviation of the population (σ) = 17
Sample size (n) = 36
1. Mean of the sample mean (μₙ):
The mean of the sample mean is the same as the mean of the population. Therefore, μₙ = μ = 95.
2. Standard deviation of the sample mean (σₙ):
To find the standard deviation of the sample mean, divide the standard deviation of the population by the square root of the sample size:
σₙ = σ / √(n)
Now, let's substitute the given values:
σₙ = 17 / √(36)
Simplifying:
σₙ = 17 / 6
Therefore, the standard deviation of the sample mean (σₙ) is approximately 2.83.
In summary:
Mean of the sample mean (μₙ) = 95
Standard deviation of the sample mean (σₙ) ≈ 2.83