A random variable X is uniformly distributed over the interval (48, 96).
Find the following probabilities.
a) P(50 < X < 70)
b) P(X < 75)
c) P(X > 90)
d) P(X < 60 or X > 80)

a)

b)

c)

d)

And using the CDF we got:

And using the CDF and the complement rule we got:

So then the probability required would be:

P(X < 60 or X > 80) = 0.25+0.333= 0.583

Step-by-step explanation:

For this case we define the random variable of interest X, and we know the distribution given by:

The density function is given by:

And the cumulative distribution function is given by:

Part a

We want this probability:

And we can find this probability with this difference:

And replacing we got:

Part b

We want this probability:

And using the CDF we got:

Part c

We want this probability:

And using the CDF and the complement rule we got:

Part d

And using the CDF we got:

And using the CDF and the complement rule we got:

So then the probability required would be:

P(X < 60 or X > 80) = 0.25+0.333= 0.583

it is 10.6 according to my calculations

soo this can be solve by using the formula:

f = p( 1 + i)^ n

where f is the future profit

p is the initial profit

i is the percent increase

n is the number of years

a . f = 30000 ( 1.05)^n

b. f = 30000 ( 1.05)^15

f = $62,368