Chapter 7: The Central Limit Theorem

If the sample size is large enough then we can assume it has an approximately normal distribution.

a continuous random variable (RV) that appears when we are interested in the intervals of time between some random events

the mean of X

the standard deviation of X

If you draw random samples of size n, then as n increases, the random variable 𝑥 which consists of sample means, tends to be normally distributed

approaches a normal distribution as n, the sample size, increases.

𝜎𝑥 = 𝜎𝑋 / √𝑛 =standard deviation of x¯

As sample sizes increase, the distribution of means more closely follows the normal distribution.

∑X ~ N[(n)(μx),(𝑛√n)(σx)]

has a mean equal to the original mean multiplied by the sample size and a standard deviation equal to the original standard deviation multiplied by the square root of the sample size.

𝛴𝑥–(𝑛)(𝜇𝑋) / (√𝑛)(𝜎𝑋)

if you take samples of larger and larger size from any population, then the mean x¯ of the sample tends to get closer and closer to μ.

there are a certain number n of independent trials. the outcomes of any trial are success or failure. each trial has the same probability of a success p

is one sum.

the mean of ΣX

standard deviation of ΣX

If the sample size is large enough then we can assume it has an approximately normal distribution.

a continuous random variable (RV) that appears when we are interested in the intervals of time between some random events

the mean of X

the standard deviation of X

If you draw random samples of size n, then as n increases, the random variable 𝑥 which consists of sample means, tends to be normally distributed

approaches a normal distribution as n, the sample size, increases.

𝜎𝑥 = 𝜎𝑋 / √𝑛 =standard deviation of x¯

As sample sizes increase, the distribution of means more closely follows the normal distribution.

∑X ~ N[(n)(μx),(𝑛√n)(σx)]

has a mean equal to the original mean multiplied by the sample size and a standard deviation equal to the original standard deviation multiplied by the square root of the sample size.

𝛴𝑥–(𝑛)(𝜇𝑋) / (√𝑛)(𝜎𝑋)

if you take samples of larger and larger size from any population, then the mean x¯ of the sample tends to get closer and closer to μ.

there are a certain number n of independent trials. the outcomes of any trial are success or failure. each trial has the same probability of a success p

is one sum.

the mean of ΣX

standard deviation of ΣX