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

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

9 hours

Step-by-step explanation:

12 people take 15 hours to complete one job. First let's ask how long it would take 18 people working at the same rate to complete the same job? We can use proportions to answer this

Now we know that one job takes 18 people 22.5 hours, so 2/5 of the job would take