00:01
Hello students we are given average score of golfers as a mean and standard deviation is given.
00:07
Suppose 100 goalers played the goals today and we need to find a probability the average score of 100 golfer exceeded 75.
00:16
So let's start with that answer.
00:20
So if i write here central limit theorem which is clt, central limit theorem clt states that states that distribution of sample means distribution of sample means sample means approximate normal distribution as sample size if i write here as sample size gets larger.
01:19
What does it mean? it means that here sample size is 100.
01:24
So it means it is larger.
01:25
So it follows a normal distribution.
01:28
So normal distribution is the distribution in which all the random variables are distributed amongst bell shaped curve.
01:38
Right.
01:38
So basically if i draw for this, this is bell shaped curve, something like this, having jad value and this is minus j and this is probability value p z so if i write here z score attribute is x minus mu divided by sigma so where mu is mean and sigma is standard deviation but according to central limit theorem if i write here if crt applies crt applies then sample mean is same as this so this is mu x is equals to uh so mu is given as definitely 74 so this is same.
02:24
So if i write for sample standard deviation, sample standard deviation would be sigma x which is sigma divided by undrout of n.
02:38
So sigma is basically if i write here this is 5 divided by unrout of 100 so 5 divided by 10 which is basically 0 .5 if we are going to write here.
02:49
So in the question we are last that is the probability average score of 100 goal first exceed 75...