Question

see attachment!!!!!!!!!!!

Answer 1

A variable X has a uniform distribution on the interval from 7 to 21.

(a) What is the height of the density curve for X?

(b) What is P(13.23 X 16.15)?

(c) What is P(X > 13.43)?

(d) What is the value b such that P(b < X < 16.41) = 0.4334?

(e) What is the interquartile range of the distribution of X?

Answer 2

can you help?

Answer 3

sorry dude, i have no idea

Answer 4

uniform distribution means all points are equally likely

Answer 5

can you explain c and d

Answer 6

length from 7 to 21 is 14 so the height of the "curve" will be \(\frac{1}{14}\)

Answer 7

but really you are just computing lengths
forget the height it is silly

Answer 8

B should be 13.23 less than or equal to x less than or equal to 16.15

Answer 9

sure length from \(13.23\) so \(21\) is \(21-13.23=7.77\) so \[P(X>13.23)=\frac{7.77}{14}\] whatever that is

Answer 10

makes no difference

Answer 11

\(P(X\geq b)=P(X>b)\) for the continuous uniform distribution

Answer 12

in simple english, compute the length of the favorable interval, divide by the total length, which in your caseis 14

Answer 13

in other words, for B it is
\[\frac{16.15-13.23}{14}\]

Answer 14

for C it is
\[\frac{21-13.23}{14}\]

Answer 15

what about d

Answer 16

actually i think i made a typo, for C it should be
\[\frac{21-13.43}{14}\] but you get the idea right?

Answer 17

yes

Answer 18

for D you know know \(b\) but you know
\[\frac{16.41-b}{14}=0.4334\]so you can solve for it

Answer 19

oh , I got it . ` for the E , do I have to find median first?

Answer 20

now i cannot help, because i don't know what "interquartile range" means, sorry
maybe i can look it up

Answer 21

median is pretty clearly 14 as it is half way between 7 and 21

Answer 22

we have to find q1 which 25 % of it and q 3 is 75% of it

Answer 23

then Interquartile range = q3 - q1

Answer 24

oh i think inter quartile range is a fancy word for the middle part right? middle half

Answer 25

yeah what you wrote

Answer 26

length is 14, divide in to 4 get 3.5

Answer 27

is it 13?

Answer 28

it is a range, not a number

Answer 29

\(7+3.5=10.5\) and \(21-3.5=17.5\) so the middle half of the interval is \((10.5,17.5)\)

Answer 30

yeah, but if you wrote the number in order like 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Answer 31

at least i think that is right

Answer 32

obivously the median is 14

Answer 33

this is a continuous distribution, not discrete

Answer 34

then we look at the half from 7 to 14

Answer 35

10 is going to be first median? which 25 %

Answer 36

18 is going to be 75 %

Answer 37

am I right?

Answer 38

\(X\) can take on any value
decimals, fractons, irrational number etc

Answer 39

no it is the entire interval from 7 to 21, which has length 14, divided in to 4 equal parts
not integers

Answer 40

so it's going to be 7

Answer 41

this question can be interpreted as follows:
divide the interval in to 4 equal parts, take the middle two

Answer 42

17.5-10.5

Answer 43

don't forget it is asking for an inter quartile Range not a number

Answer 44

yes

Answer 45

i would say 10.5 to 17.5

Answer 46

ok got it

Answer 47

good! good luck

Answer 48

wait for the c i got 0.555, but its wrong

Answer 49

I got the answer, thanks `