Exam 8: Continuous Probability Distributions

Electronics Test the time it takes a student to finish a electronics test has a uniform distrubtion between 50 and 70 minutes. -{Electronics Test Narrative} What is the mean amount of time it takes a student to finish the test?

Which of the following represents a difference between continuous and discrete random variables?

The probability that a standard normal random variable Z is less than −3.5 is approximately 0.

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 between 80 and 90?

A ² distribution with 5 degrees of freedom has a mean of ____________________ and a variance of ____________________.

Suppose X has a normal distribution with mean 10 and standard deviation 2.The probability that X is less than 8 is equal to the probability that Z is less than ____________________.

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?

Light Bulb Lifetime The lifetime of a light bulb (in hours)is exponentially distributed with λ = 0.008. ​ ​ -{Light Bulb Lifetime Narrative} Find the probability that a light bulb will last between 120 and 140 hours.

Z_.025 is the value of Z such that the area to the ____________________ of Z is .9750.

We standardize a random variable by subtracting its ____________________ and dividing by its ____________________.

The value of an F distribution with v₁ = 6 and v₂ = 9 degrees of freedom such that the area to its right is 0.05 is 3.37.

Suppose X has a normal distribution with mean 70 and standard deviation 5.The 50th percentile of X is 70.

The sum of all values of f(x)over the range of [a,b] must equal one.

Repair Time The time it takes a technician to fix a telephone problem is exponentially distributed with a mean of 15 minutes. ​ ​ -{Repair Time Narrative} What is the variance of the time it takes a technician to fix a telephone problem?

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?

If X has a normal distribution with mean 60 and standard deviation 6,which value of X corresponds with the value z = 1.96?

____________________ the value of σ in a normal distribution will make it wider.

Use the F table to find the following values of F. a.F_.99,12,20 b.F_.95,20,40 c.F_.975,5,15 d.F_.99,8,30

What number corresponds to ?

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