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Tju [1.3M]
3 years ago
7

The time (in minutes) until the next bus departs a major bus depot follows a uniform distribution from 25 to 46 minutes. Let X d

enote the time until the next bus departs. The distribution is and is . The mean of the distribution is μ= . The standard deviation of the distribution is σ= . The probability that the time until the next bus departs is between 30 and 40 minutes is P(30
Mathematics
2 answers:
ch4aika [34]3 years ago
5 0

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

SCORPION-xisa [38]3 years ago
3 0

Answer:

The distribution is uniform and is continuous probability distribution.

The mean of the distribution is μ= <u>35.5 minutes</u>.

The standard deviation of the distribution is σ= <u>6.06 </u>

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<u> uniform</u> and is <u>continuous probability distribution.</u>

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= <u>35.5 minutes</u>.

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= <u>6.06 </u>

d. P(30<x<40)

<em>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) .</em>

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  

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