Exam 17: Continuous Random Variables

If X has density function f(x)= find k.

The random variable X has density function f(x)= Find (a)P and (b)P .

Suppose X is uniformly distributed over the interval .Find P(3 < X < 8).

If Z has a standard normal distribution,find P(-0.65 < Z < 1.92).

Suppose the cumulative distribution function for the random variable X is given by F(x)= Find P(1 < X < 3).

The random variable X has density function f(x)= Find the cumulative distribution function F over .

If Z has a standard normal distribution,find P(-3 ≤ Z ≤ -0.5).

Suppose X has binomial distribution with n = 100 and p = 0.1.Using the normal approximation,find (a) and (b)

If X is normally distributed with μ = 20 and σ = 4,find P(16 ≤ X ≤ 18).

If Z has a standard normal distribution,find P(2.2 < Z < 3.5).

A manufacturing plant claims that only 0.2% of its products are defective.From a sample of 3000 products,it is found that 4 are defective.Using n = 3000 and p = 0.002,approximate P(X = 4)by using the normal approximation.

If X has density function f(x)= find σ.

If X is normally distributed with μ = 18 and σ = 2,find P(11 ≤ X ≤ 16).

If X is normally distributed with μ = 80 and σ = 8,find P(X < 74).

If X is a normal random variable with μ = 16 and σ = 2,determine the Z-value that corresponds to X = 23.

The random variable X has density function f(x)= Find the cumulative distribution function F over .

If X is uniformly distributed over ,what is the density function for X?

The life expectancy (in years)of a computer printer is distributed exponentially with k = .If the printer's warranty lasts 3 years,what is the probability that a printer will last more than 10 years?

The length of time (in minutes)that a person arriving at a bus stop must wait for a bus is uniformly distributed with density function f(x)= where 0 ≤ x ≤ 15.Find the mean waiting time and the standard deviation.

If Z has a standard normal distribution,find P(|Z| > 1.75).