![]() ![]() Therefore, based on the information provided, it is concluded that \( \Pr(11.3 \leq \bar X \leq 12.4) = 0.4759\). n\), then \(\bar X\) is normallyĭistributed with the same common mean \(\mu\), but with a variance of \(\displaystyle\frac\] ![]() REMEMBER: The z-table ALWAYS gives you the probability of LESS THAN. How do you calculate sampling distribution?Īssuming that \(X_i \sim N(\mu, \sigma^2)\), for all \(i = 1, 2, 3. Therefore, the probability that a sample of 100 people will eat an average of at least 503 chocolates in a year is about 6.68. Quartiles divide an ordered dataset into four equal. The distribution of \(\bar X\) is commonly referred as to theĪnother name you will see the normal distribution referred about is the gaussian distribution, or the bell-shaped distribution. On a number line, you can see that the range of values for Dataset B is larger than Dataset A. Since any linear combination of normal variables is also normal, the sample mean \(\bar X\) is also normallyĭistributed (assuming that each \(X_i\) is normally distributed). , X_n\) is averaged, we get the sample mean When a sequence of normally distributed variables \(X_1, X_2. If you wanted to have a more 'exact' answer, you could use the Binomial distribution. But it's important to remember, that treating p as Normally distributed is an approximation (albeit a quite good one most of the time). More About this Normal Distribution Probability Calculator for Sampling Distributions Tool 2 Answers Sorted by: 1 DeepSea's answer is a pretty standard way to do this. ![]()
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