The random-number generator is used to generate a real number at random between 0 and 1, equally likely to fall anywhere in this interval of values. (For instance, 0.3794259382... is a possible outcome.) a. Sketch a curve of the probability distribution of this random variable. b. What is the mean of this probability distribution? c. Find the probability that the random number falls between 0.35 and 0.6. d. Find the probability that the random number is less than 0.81.

Step-by-step explanation:

f(x)=1, 0 < x < 1 is the probability density function of the random variable x.

generally, it is f(x)=1/(b-a)  a < x < b;

where b=1 and a=0.

b) mean = integral (0 to 1) xdx  = (0 to 1)  = 1/2

c)integral( 0.35 to 0.6) dx  =x (between 0.35 and 0.6)  = 0.6-0.35=0.25

d) integral(less than 0.82)dx = x (between 0 and 0.81) = 0.81 - 0 = 0.81

4 hours

Step-by-step explanation:

Laine reads 25 pages in 30 minutes.

We have to calculate how long it will take to read 200 pages by unitary method.

∵ Laine reads 25 pages in 30 minutes

∴ Laine reads 1 page in =

She reads 200 pages in =   × 200

                                         = 240 minutes

Now we convert 240 minutes in hours

60 minutes = 1 hour

240 minutes = 240 / 60 = 4 hours

Laine takes 4 hours to read 200 pages.