Question

your ariswe (22) Explain the difference between standard normal distribution and student's t distribution.(10 points)

Answer 1

Difference between standard normal distribution and student's t distribution :

The standard normal distribution is a specific distribution with mean (0)and variance (1) . This is the distribution that is used to construct tables of the normal distribution.

i.e. z = ( X - mu ) / sigma

Check a value of z-score is in standard normal distribution table ( or it's means z table ).

When the sample size is large ( n >= 30 ) and the population follows standard normal distribution.

If the population standard deviation is known then uses standard normal distribution.

Student's t-distribution (or simply the t-distribution) is any member of a family of continuous probability distributions that arises when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown.

When the sample size is small (n <= 30) and the population follows normal distribution usually we uses t-distribution

If the population standard deviation is unknown then we uses the t-distribution.