(Solved): Let Y be a random variable. In a population, Y=116 and Y2=58. Use the central limit theor ...

Let $Y$ be a random variable. In a population, ${\mu }_Y=116$ and ${\sigma }_Y^2=58$. Use the central limit theorem to answer the following questions. (Note: any intermediate results should be rounded to four decimal places) In a random sample of size $\mathrm{n}=153$, find $\mathrm{Pr}(\bar{Y}<119)$. $\mathrm{Pr}(\bar{Y}<119)=$ (Round your response to four decimal places) In a random sample of size $\mathrm{n}=112$, find $\mathrm{Pr}(118<\bar{Y}<121)$. $\mathrm{Pr}(118<\bar{Y}<121)=$ (Round your response to four decimal places) In a random sample of size $\mathrm{n}=188$, find $\mathrm{Pr}(\bar{Y}>118)$. $\mathrm{Pr}(\bar{Y}>118)=$ (Round your response to four decimal places)