Probability of sample means

Answer

Sample Mean

The sample mean is a statistic that is used to estimate a population's mean. Even with smaller samples, if the population is normally distributed, the sample means will be normally distributed.

An average of a group of data is referred to as a sample mean. A data set's central tendency, standard deviation, and variance can all be calculated using the sample mean. The sample mean has a wide range of applications, including determining population averages.

 Probability of sample means

For example, The height of 25 students is collected in a class. Notably, the data has a $\delta =10 and \mu =40$. Calculate the probability that a sample mean will be greater than 45.

This means that $P(\stackrel{-}{X}>45)$

Recall that; $z=\frac{{\displaystyle \stackrel{-}{X}}-\mu }{{\displaystyle \frac{\delta }{\sqrt{n}}}}$

$z=\frac{{\displaystyle 45-40}}{{\displaystyle \frac{10}{\sqrt{25}}}}$

$=\frac{5}{2}=2.5$

Therefore, the probability that the sample mean will be greater than 45 can be said to be the probability that z is greater than 2.5.

Using the z-tables to find the probability;

We have: $P(\stackrel{-}{X}>45)= P(z>2.5)$

$=0.99379$$=1-0.99379=0.00621$

$=0.621\%$

Yes · 0 No · 0 Add Comment · 0

Add ·

Report