16.06 The central limit theorem
Interactive practice questions
The weights of eggs at a particular egg farm are determined to be normally distributed with a mean of $65.7$65.7 grams and a standard deviation of $1.2$1.2 grams.
Many egg samples of size $100$100 are taken and measured, and the means of each of the samples, $\overline{X}$X are calculated.
What type of distribution does $\overline{X}$X represent?
Exponential Distribution
Discrete Uniform Distribution
Normal Distribution
Continuous Uniform Distribution
Calculate the mean of $\overline{X}$X.
Calculate the standard deviation of $\overline{X}$X corresponding to a sample size of $100$100. Round your answer to $2$2 decimal places.
Consider a fair $6$6 sided dice, with faces labeled from $1$1 to $6$6. Let $X$X be the outcome when the dice is rolled.
The amount of black coffee dispensed by an automatic coffee machine varies uniformly between $283$283 ml and $311$311 ml.
Let $X$X be the amount of coffee dispensed in a cup.
A discrete random variable $Y$Y has a mean of $50$50 and a standard deviation of $3.6$3.6. Many samples of $52$52 observations are taken and the means $\overline{Y}$Y for each sample calculated.