Exam 17: Continuous Random Variables

The random variable X has density function f(x)= Find P(X > 2).Give answer in terms of e.

If Z has a standard normal distribution,find P(Z > -1.81).

If Z has a standard normal distribution,find P(-2 ≤ Z ≤ -1).

The scores on an examination are normally distributed with μ = 500 and σ = 100.What percentage of the scores are less than 360?

If X is normally distributed with μ = 25 and σ = 5,find P(20 ≤ X ≤ 35).

The life expectancy (in years)of patients after they have contracted a certain disease is exponentially distributed with k = 0.4.Find the mean life expectancy and the standard deviation.

The length of time (in minutes)that a person arriving at a train station must wait for a train is uniformly distributed with density function f(x)= where 0 ≤ x ≤ 20.Find the mean waiting time and the standard deviation.

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

Suppose the time (in minutes)applicants must wait to receive a driver's examination is uniformly distributed with density function f(x)= where 0 ≤ x ≤ 40 and f(x)= 0 elsewhere.What is the probability that an applicant must wait less than 25 minutes?

If X is normally distributed with μ = 8 and σ = 2,find P(3 ≤ X ≤ 8).

If X is normally distributed with μ = 50 and σ = 10,find such that P(X < )= 0.9938.

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 break down during the warranty period?

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

If X is normally distributed with μ = 12 and σ = 2,find P(12 ≤ X ≤ 15).

If X is normally distributed with μ = 10 and σ = 2,find P(4 ≤ X ≤ 12).

If X is normally distributed with μ = 40 and σ = 6,find P(X ≥ 37).

The life (in hours)of light bulbs of a certain brand is normally distributed with mean 1200 and standard deviation 100.What percentage of such bulbs will burn more than 1250 hours?

If X is normally distributed with μ = 100 and σ = 10,find P(X < 115).

Suppose the time (in minutes)applicants must wait to receive a driver's examination is uniformly distributed with density function f(x)= where 0 ≤ x ≤ 40 and f(x)= 0 elsewhere.What is the probability that an applicant must wait more than 35 minutes?

Suppose X is normally distributed with mean 80 and standard deviation 15.Without using tables,determine the approximate value of P(65 < X < 95).