Answer:
Step-by-step explanation:
Previous concepts
Normal distribution, is defined as a symmetric "probability distribution centered around the mean, indicating that values near the mean are more common than those further away".
The Z-score measures a value's relation to the mean of a set of values, displayed in terms of how many standard deviations away it is from that mean.
According to the central limit theorem, "with a population having mean μ and standard deviation σ, if we draw sufficient random samples from this population with replacement, the means of those samples will resemble a normal distribution, regardless of the original population's shape, as long as the sample size is large enough".
Solution to the problem
In this scenario, we select a sample size of n = 100
The central limit theorem informs us that the distribution of the sample mean is defined by:
Thus, the mean for the sample would be:
And the standard deviation would be: