91影视

Given in the question that,

population mean$\left(渭\right)=298$$\left(渭\right)=298$

Population standard deviation $\left(蟽\right)=3$

we have to find that the probability that in individual bottle contains less than $295ml$.

The formula to compute the Z- score is:

$z=\frac{x-渭}{蟽}$

$x$is raw score

$渭$is population mean

$s$is population standard deviation

Consider, $X$be the random variable that shows the amount of cola in plastic bottles follows the normal distribution with mean $=298ml$and standard deviation $=3ml$.

The probability that an individual bottle would contain less than$295ml$cola can be computed as:

$P(X<295)=P\left(\frac{x-渭}{蟽}<\frac{195-渭}{蟽}\right)$

$=P\left(Z<\frac{295-298}{3}\right)$

$=P(Z<-1)(Froms\tan dardnormaltable)$

$=0.1587$

Thus, the required probability is $0.1587$.

Given in the question that sample size$\left(n\right)=6$we have to find that the probability that the mean contents of six randomly selected bottles is less than $295ml$.

The probability that mean content in randomly chosen $6$bottles is less than $295ml$is calculated as follows:

$P(\stackrel{炉}{X}<295)=P\left(\frac{{\displaystyle \frac{\overline{x-渭}}{蟽}}}{\sqrt{n}}<\frac{{\displaystyle \frac{295-渭}{蟽}}}{\sqrt{n}}\right)$

$=$$P\left(Z<\frac{{\displaystyle \frac{295-298}{3}}}{\sqrt{6}}\right)$

$P(Z<-2.45)(Froms\tan dardnormaltable)$$=P(Z<-2.45)(Froms\tan dardnormaltable)$

$=0.0071$

Thus the require probability is$0.0071$