91Ó°ÊÓ

Given in the question that, Yoonie is a personnel manager in a large corporation. Each month she must review $16$ of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of $1.2$ hours. Let $\mathrm{Î\S }$ be the random variable representing the time it takes her to complete one review. Assume $\mathrm{Î\S }$ is normally distributed. Let role="math" localid="1648619084184" $\stackrel{¯}{x}$be the random variable representing the mean time to complete the re$16$views. Assume that the$16$reviews represent a random set of reviews.

According to the provided details, the time for each review $\left(X\right)$is normally distributed, the meantime for each review is $4$hours and the standard deviation is $1.2$hours and the sample size is $16$employees.

The normal distribution with mean $\left(\mathrm{μ}\right)$and standard deviation $\left(\mathrm{σ}\right)$is given as:

$X~N(\mathrm{μ},\mathrm{σ})$

So, the distribution time for each review $\left(X\right)$is given as below:

$X~N(4,1.2)$

$X~N(4,1.2)$

Given in the question that, Yoonie is a personnel manager in a large corporation. Each month she must review $16$of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of$1.2$hours. Let$\mathrm{Î\S }$be the random variable representing the time it takes her to complete one review. Assume $\mathrm{Î\S }$is normally distributed. Let $\stackrel{¯}{x}$be the random variable representing the mean time to complete the $16$reviews. Assume that the $16$reviews represent a random set of reviews.

According to the provided details, the time for each review$\left(X\right)$is normally distributed, the meantime for each review is $4$hours and the standard deviation is $1.2$hours and the sample size is $16$employees.

The distribution for the sample mean $\left(\stackrel{¯}{X}\right)$is given as below:

role="math" localid="1648622435181" $\stackrel{¯}{X}~N\left(\mathrm{μ}x,\frac{\mathrm{σ}x}{\sqrt{n}}\right)$

role="math" localid="1648622812034" $\stackrel{¯}{X}~N\left(4,\frac{1.2}{\sqrt{16}}\right)$

$\stackrel{¯}{x}~N\left(4,0.3\right)$

$\stackrel{¯}{x}~N\left(4,0.3\right)$