Probability : Acceptable Range of Values and Cumulative Distribution Function

1) A manufacturer of flashlight batteries wishes to control the quality of its product by rejecting any lot in which the proportion of batteries having unacceptable voltage appears to be too high. To this end, out of each large lot (10,000 batteries), 25 will be selected and tested. If at least 5 of these generate an unacceptable voltage, the entire lot will be rejected. What is the probability that a lot will be rejected if...
a) 5% of the batteries in the lot have unacceptable voltages?
b) 10% of the batteries in the lot have unacceptable voltage?
c) 20% of the batteries in the lot have unacceptable voltage?

2) The weekly demand for propane gas (in 1000s of gallons) from a particular facility is an rv X with pdf {see attachment}

a) Compute the cdf of x
b) Obtain an expression for the (100p)th percentile. What is the value for m??
c) Compute E(x) and V(x)
d) If 1.5 thousand gallons are in stock at the beginning of the week and no new supply is due during the week, how much of the 1.5 thousand gallons is expected to be left at the end of the week?

Probability Density function, Probabilitydistribution, andProbability
Could someone give me definitions with examples of each.
Please make the explanations as clear as possible.

4. The probability density function if X, the lifetime of a certain type of electronic device (measured in hours} is given by:
f(x) =
10/x^2 for x>10
and
=0 for x<=10
(a) Find P {X > 20}
(b) What is the cumulativedistributionfunction of X?
(c) What is the probability that of 6 such types of devices at least 3 will

#4. The probability density function of X, the lifetime of a certain type of electronic device (measured in hours), is given by
f (x) = 10/x2 x > 10
f (x) = 0 x ≤ 10
(a) Find P{X > 20}.
(b) What is cumulativedistributionfunction of X?
.. (see attachment)

Let X denote a continuous random variable with probability density function f(x) = kx^3/15 for 1≤ X ≤ 2.
a. Determine the value of the constant k.
b. Determine the probability that X > 1.5.
c. Determine the cumulativedistributionfunction F(x) and state the values of F(x) at x = 0.5, 1.5, and 2.5.

This problem is about the uniform probabilitydistribution.
The probability density f(x) = 0 up to point a then equals 1/(b-a) up to the point b. The lower limit is the point a and b is the upper limit of the x values.
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I need help with the following questions:
1. Sketch in Exc

Show that if the value of a variable x is selected by inverting the cdf (cumulative density function), x = F^-1 (RN), the distribution of the x values is given by the function f(x).
See attached file for full problem description.

Consider the following exponential probability density function:
F(x) = (1/14)e^(-x/14) for x>=0
This number represents the time between arrivals of customers at the drive-up window of a bank.
a. Find f(x<=7)
b. Find f(3.5<=x<=7)

1) Let X be a discrete random variable with probability mass function Pr{X=k}= c/(1+(k^2)) for k= -2,-1, 0, 1, 2.
a) determine Pr{x <= 0}
(b) Determine the mean of X
(c) Determine all medians of X
(d) Compute Pr{X=2 | X >= 0}
(e) Determine the cumulativedistributionfunction

You are told that the continuous random variable X is exponentially distributed with parameter a (a > 0). A standard result then says that the probability density function of X is (see attachment)
f(x) = aexp(-ax) for x > 0.
Use this to prove that the corresponding cumulativedistributionfunction F(x) (sometimes referred