(a) <em>X</em> has a probabiliity density of
If the lower quartile is 5 and the upper quartile is 9, then
Computing the integrals gives the following system of equations:
5 - <em>a</em> = 0.25 (<em>b</em> - <em>a</em>) ==> 0.75<em>a</em> + 0.25<em>b</em> = 5 ==> 3<em>a</em> + <em>b</em> = 20
<em>b</em> - 9 = 0.25 (<em>b</em> - <em>a</em>) ==> 0.25<em>a</em> + 0.75<em>b</em> = 9 ==> <em>a</em> + 3<em>b</em> = 36
Eliminate <em>a</em> :
(3<em>a</em> + <em>b</em>) - 3 (<em>a</em> + 3<em>b</em>) = 20 - 3×36
-8<em>b</em> = -88
==> <em>b</em> = 11 ==> <em>a</em> = 3
and so P(<em>X</em> = <em>x</em>) = 1/(11 - 3) = 1/8 for all 3 < <em>x</em> < 11.
(b)
(c) The distribution function is then
If they are congruent then they are equal
7x-40=4x+32
7x-4x=32+40
3x=72
x=24
Answer:
3/2
Step-by-step explanation:
Jacob's (12) to Mark's (8) would be 12 to 8. We want to simplify this. We can divide both numbers by 4 to get 3 to 2. In fraction form would be 3/2.
20% of 30
Or .20×30 and you'll get your answer
Answer:
The box-and-whisker plot for the given question is as shown at the attached figure.
Minimum = 11
Lower quartile = Q1 = 12
Median = Q2 = 23.5
Upper quartile = Q3 = 27
Maximum = 33
<u>So, according to the given data and the figure:</u>
- The box will go from <u>12 to 27</u> ⇒ Q1 to Q3
- A line dividing the box will go at <u>23.5</u> ⇒ Q2
- The left whisker will go from <u>11 to 12</u> ⇒ Minimum to Q1
- The right whisker will go from to <u>27 to 33</u> ⇒ Q2 to Maximum