## yashar806 2 years ago A variable X follows a normal distribution with mean 10 and standard deviation 5. Another variable Y follows a normal distribution with mean 25 and standard deviation 10. The maximum height of the density curve for X is_______ (i) the maximum height for the density curve for Y , and the area under the density curve for X is__________ (ii) the area under the density curve for Y . (A) (i) greater than, (ii) less than (B) (i) less than, (ii) greater than (C) (i) equal to, (ii) equal to (D) (i) greater than, (ii) equal to (E) (i) less than, (ii) less than

1. UnkleRhaukus

there is something missing from your question

2. yashar806

no its the actual question

3. yashar806

4. yashar806

check that one

5. yashar806

are u there?

6. UnkleRhaukus

you have to compair the standard deviations of each curve, remember that the sum of areas under each curve is one

7. yashar806

but , how ? could you explain it?

8. UnkleRhaukus

|dw:1363240984062:dw|

9. UnkleRhaukus

theses are two normal curves with the same mean , but different std.div

10. UnkleRhaukus

the both have the same area ,; the sum of densities is one

11. yashar806

there are not same mean?

12. UnkleRhaukus

can you tell be which curve has the greatest std. div , the red or black curve

13. yashar806

red?

14. UnkleRhaukus

right , because less of the red is as close the mean as the black

15. UnkleRhaukus

now if the means are different will this effect which is taller ?

16. yashar806

no

17. UnkleRhaukus

right , the maximun height of the curve is only dependent of the std.div

18. UnkleRhaukus

So Y has a std.div of 10 and X has a std.div of 5

19. UnkleRhaukus

something like this |dw:1363241494740:dw|

20. yashar806

so x has higher density curve ?

21. yashar806

and the area under the density curve for X is less then (ii) the area under the density curve for Y .

22. yashar806

is that righ?

23. yashar806

hello?

24. UnkleRhaukus

x has higher density ✓

25. UnkleRhaukus

remember that the area under each density curve must sum to one

26. yashar806

so its same

27. yashar806

euqal

28. UnkleRhaukus

yerh

29. yashar806

thank you so much

30. yashar806

i got it

31. UnkleRhaukus

does it make senses now?

32. yashar806

yes thanks

33. UnkleRhaukus

cool