Answer:
Step-by-step explanation:
The distribution is Uniform and is continuous.
We are given a = 25 and b = 446
The mean of the distribution is
Mean = µ = (a + b) / 2
= (25 + 44) / 2
= 34.5
The standard deviation of the distribution is
SD = σ = (b – a) / sqrt(12)
= (46 – 25) / sqrt(12)
= 21/3.464102
= 6.062minutes
SD = σ = 6.062minutes
Now, we have to find P(30<X<40)
P(30<X<40)
= (40 – 30) / (46 – 25)
= 10/19
= 0.4762
Required probability = 0.4762
Now, we have to find the value of a for which P(X≤a) = 0.9
We have, P(X≤a)
= (a – 25) / (46 – 25)
= (a – 25) / 21
(a – 25) / 21 = 0.9
(a – 25) = 0.9*21
So, a = 18.9 + 25 = 43.
a = 43.9
= 43.9minutes
Answer:
The distribution is uniform and is continuous probability distribution.
The mean of the distribution is μ= 35.5 minutes.
The standard deviation of the distribution is σ= 6.06
P(30<x<40)= 0.476
Step-by-step explanation:
a.The amount of time in minutes until the next bus departs is uniformly distributed between 25 and 46 inclusive.
The distribution is uniform and is continuous probability distribution.
b.Let X be the number of minutes the next bus arrives and a= 25 , b= 46. Hence mean = a+b/2= 25+ 46/ 2= 35.5 minutes.
The mean of the distribution is μ= 35.5 minutes.
c. Standard deviation = √(b-a)²/12
Standard deviation= √(46-25)²/12= √(21)²/12= √441/12=√36.75= 6.06
The standard deviation of the distribution is σ= 6.06
d. P(30<x<40)
For this we draw a graph . It is also called the rectangular distribution because its total probability is confined to a rectangular region with base equal to (b-a) and height 1/(b-a) .
This can be calculated as
P(30<x<40)= base * height (in this probability the base is 10)
= (40-30) *(1/ 21)= 10/21= 0.476
