Exam 8: Continuous Probability Distributions

Stacy took a math test whose mean was 70 and standard deviation was 5.The total points possible was 100.Stacey's results were reported to be at the 95th percentile.What was Stacey's actual exam score,rounded to the nearest whole number?

The probability density function f(x)of a random variable X that has a uniform distribution between a and b is

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.

IT Graduates Salary The recent average starting salary for new college graduates in IT systems is $47,500.Assume salaries are normally distributed with a standard deviation of $4,500. -{IT Graduates Salary Narrative} What percent of starting salaries are no more than $42,250?

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

What number corresponds to $\chi _ { 0.05,12 } ^ { 2 }$ ?

If X has an exponential distribution with parameter $\lambda$ ,then the mean of X is ______________.

Which of the following is true for an exponential distribution with parameter $\lambda$ ?

The variance of a Student t distribution approaches ____________________ as the degrees of freedom increase to infinity.

The mean and standard deviation of an exponential random variable are equal to each other.

You can use a continuous random variable to ____________________ a discrete random variable that takes on a countable,but very large,number of possible values.

If X is a continuous random variable on the interval [0,10],then P(X > 5)= P(X $\ge$ 5).

Continuous probability distributions describe probabilities associated with random variables that are able to assume any finite number of values along an interval.

A random variable X has a normal distribution with a mean of 250 and a standard deviation of 50.Given that X = 175,its corresponding value of Z is -1.50.

If the mean of an exponential distribution is 2,then the value of the parameter $\lambda$ is 2.0.

IT Graduates Salary The recent average starting salary for new college graduates in IT systems is $47,500.Assume salaries are normally distributed with a standard deviation of $4,500. -{IT Graduates Salary Narrative} What is the probability of a new graduate receiving a salary between $45,000 and $50,000?

Like that of the Student t distribution,the shape of the chi-squared distribution depends on its number of degrees of freedom.

A continuous probability distribution represents a random variable having an infinite number of outcomes which may assume any number of values within an interval.

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.

Counter Sales Suppose that customers arrive at a counter at an average rate of three customers per minute and that their arrivals follow the Poisson model. -{Counter Sales Narrative} Use the appropriate exponential distribution to find the probability that the next customer will not arrive within the next 2 minutes.