00:01
Hello show ands we need to write here at one theater movie course spend a mean of 6 .32 on refreshment with standard deviation of 2 .55 what is the probability that the mean amount spent on refreshment by a random sample of 50 movie course will be between 6 and 7 we need to write so we are given here normal distribution if i write for this normal distribution so basically if i write here for this all the random variables are distributed amongst whale shaped curve so if i draw for this all the random variables are distributed amongst whale shaped curve this is plus jr this is minus z this is probability p z and total area under normal distribution curve is one it means sum of all probabilities under normal distribution curve is 1.
01:01
Right hand side area is 0 .5, left hand side area is 0 .5.
01:05
It means area is symmetric about y -axis.
01:08
So basically, z -score attribute is x minus mu divided by sigma.
01:14
So if i write here for this, if i write here for this, standard sample standard deviation, here what we are given sample sizes greater so we need to apply central limit theorem so according to central limit theorem we need sample standard deviation in this case and sample mean too so what is our sample standard deviation which is sigma x is equals to sigma divided by root of n so basically sigma value is 2 .55 divided by under root of 50.
02:01
So this is 0 .361.
02:07
So if i write here for this, what would be our sample mean? sample mean value is mu as which is, so if i write here for this, sample mean is 6 .32.
02:21
So basically, jade score attribute we need to calculate for this.
02:25
So we need our probability value which is between these values.
02:31
So z1 value would be x minus 6 minus 6 .32 divided by sigma which is 0 .361 and in jad 2k 7 minus 6 .32 divided by 0 .361...