Exam 8: Continuous Probability Distributions

If X has an exponential distribution,the possible values of X are from ____________________ to infinity.

The probability that Z is less than −2 is the same as one minus the probability that Z is greater than +2.

A worker earns $16 per hour at a plant and is told that only 5% of all workers make a higher wage.If the wage is assumed to be normally distributed and the standard deviation of wage rates is $5 per hour,find the average wage for the plant workers per hour.

Suppose X is a continuous random variable for X between a and b. b.Then its probability ____________________ function must non-negative for all values of X between a and

The Student t distribution with parameter v = 2 has a mean E(t)equal to:

A random variable with density function e−x for x ≥ 0 has an exponential distribution with λ = ____________________.

Calculus Scores Scores of high school students on a national calculus exam were normally distributed with a mean of 86 and a standard deviation of 4. (Total possible points = 100.) ​ ​ -{Calculus Scores Narrative} What is the probability that a randomly selected student will have a score of 80 or higher?

Battery Life A certain brand of batteries has a lifetime that has a normal distribution with a mean of 3,750 hours and a standard deviation of 300 hours. ​ ​ -{Battery Life Narrative} What proportion of these batteries will last for more than 4,000 hours?

Given that Z is a standard normal random variable,a negative value of Z indicates that the standard deviation of Z is negative.

Subway Waiting Time At a subway station the waiting time for a subway is found to be uniformly distributed between 1 and 5 minutes. ​ ​ -{Subway Waiting Time Narrative} What is the probability of waiting no more than 3 minutes?

To be a legitimate probability density function,all possible values of f(x)must lie between 0 and 1 (inclusive).

Which of the following is not a characteristic for a normal distribution?

Counter Sales suppose that customers arrive at a counter at an avarage rate of three customers per minute and their arrivals follow the poisson model. -{Counter Sales Narrative} Write the probability density function of the distribution of the time that will elapse before the next customer arrives.

A larger standard deviation of a normal distribution indicates that the distribution becomes:

In practice,we frequently use a continuous distribution to approximate a discrete one when the number of values the variable can assume is countable but large.

If X has an exponential distribution with parameter λ,then f(0)= ____________________.

A continuous random variable is one that can assume an uncountable number of values.

If a point y lies outside the range of the possible values of a random variable X,then f(y)must equal zero.

The F distribution has two parameters called degrees of freedom,ν₁ and ν₂.We call ν₁ the ____________________ degrees of freedom,and we call ν₂ the ____________________ degrees of freedom.

If the random variable X is exponentially distributed with parameter λ = 0.05,then the variance of X,σ² = V(X)= 20.