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Sandstone is mined from two different quarries. Let $X=$ the amount mined (in tons) from thefirst quarry in one day and $Y=$ the amount mined (in tons) from the second quarry in one day.The variables $X$ and $Y$ are independent, with $\mu_{X}=12, \sigma_{X}=4, \mu_{Y}=10, \sigma_{Y}=3$(a) Find the mean and standard deviation of the variable $X+Y,$ the total amount of sandstonemined in a day.(b) Find the mean and standard deviation of the variable $X-Y,$ the difference in the mines'outputs in a day.(c) The manager of the first quarry sells sandstone at $\$ 25 / t$ , while the manager of the secondquarry sells sandstone at $\$ 28 / t .$ Find the mean and standard deviation for the combinedamount of money the quarries generate in a day.(d) Assuming $X$ and $Y$ are both normally distributed, find the probability the quarries generatemore than $\$ 750$ revenue in a day.

Intro Stats / AP Statistics

Chapter 4

Joint Probability Distributions and Their Applications

Section 1

Jointly Distributed Random Variables

Probability Topics

The Normal Distribution

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