4) Suppose x is a random variable best described by a uniform probability distribution with a = 20 and b = 40. Find P(x < 40). 5) Suppose x is a uniform random variable with a = 10 and b = 70. Find P(x > 34). 6) Suppose x is a random variable best described by a uniform probability distribution with a = 20 and b = 40. Find P(x > 40)

Chains "A" and "B" are made of the same steel. "A" consists of three links and "B" consists of six links, each link having a normal distribution function of the resisting strength with a mean of 60,000 psi and standard deviation of 5,000 psi. Determine which chain is generally weaker (from a probabilistic point of view) by plotting the probability distribution functions of their resisting strengths on the same diagram.

Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 21 days and a standard deviation of seven days. (a) In words, define the random variable X. Edit Insert - Formats - B A く) (b) Find the ZSCore for a trial lasting 20 days. (Round your answer to three decimal places.) (c) If one of the trials is randomly chosen, find the probability that it lasted at least 20 days. (d) Shade the area corresponding to this probability in the graph below. (Hint: The x-axis is the z-score. Use your z-score from part (b), rounded to one decimal place).

Let X denote the random variable that gives the sum of the faces that fall uppermost when two fair dice are cast. Find P ( X = 5 )

If life length  ( in hours )  of certain kind of device follows chi - squared distribution with dof  10 .  Find the probability that exactly  2  of  6  such devices in a system will have to be replaced within the first  16  hours of operation. Assume that life of the devices are independent

If the number X of particles emitted during a 1-hour period from a radioactive source has a poisson distribution with parameter equal to 4 and that the probability that any emitted is recorded is p=0.9 find the probability distribution of the number Y of the particles recorded in a 1-hour and hence the probability that no particle is recorded

Suppose that the age of a randomly selected business major can be considered to be a random variable with mean 20 years and standard deviation 2 years. A group of 64 business majors is selected at random and their average age x¯ is calculated. b) What is the probability that x¯< 19.7?