1 6
--- = ---
a 18
- simplify 6/18, which should be 1/3. therefore, a = 3.
Answer:
A) 2/3
B) 1/3
Step-by-step explanation:
A) Since the bus arrives uniformly at the bus stop between 10 and 10:30.Let X denote the arrival of a bus at a bus stop. Thus X is a uniform tandom variable having a density function;
f(x) = 1/30 : x ∈ [0,30]
Now, probability that a passenger arriving at the bus stop between 10 and 10:30 will have to wait more than 10 minutes can be expressed as;
P[x > 10] = ∫f(x)•dx at boundary of 30 and 10
Thus,
∫(1/30)•dx at boundary of 30 and 10
P[x > 10] = (1/30)•x at boundary of 30 and 10
P[x > 10] = (1/30)(30) - (1/30)(10)
P[x > 10] = 1 - 1/3 = 2/3
B) The probability that the passenger will have to wait additional 10 minutes is given as;
P[X > 25 | X > 15] =P[X > 25 ∩ X > 15]
= (P[X > 25])/(P[X > 15])
= [∫(1/30)•dx at boundary of 30 and 25]/ [∫(1/30)•dx at boundary of 30 and 15]
= [(1/30)•x at boundary of 30 and 25]/[(1/30)•x at boundary of 30 and 15]
= [(30/30) - (25/30)]/[(30/30) - (15/30)]
= (1 - 5/6)/(1 - 1/2)
= 1/6 ÷ 1/2 = 1/3
∩
Answer:
Axis Of Symmetry: x = 0
Vertex: (0, -6)
Domain: (
−
∞
,
∞
)
,{x
|
x
∈
R
}
Range: [
−
6
,
∞
)
,
{
y
|
y
≥
−
6
}
Answer: a) 1.029, b) (-5.318, -1.282).
Step-by-step explanation:
Since we have given that
and
So, the standard error for comparing the means :
At 95% confidence interval, z = 1.96
So, Confidence interval would be
Hence, a) 1.029, b) (-5.318, -1.282).
Here is the graph. Work is shown in the picture. I hope this helps.