Exam 8: Continuous Probability Distributions

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 less than 3,600 hours?

If the random variable X is exponentially distributed,then the mean of X will be:

A(n)____________________ random variable is one that assumes an uncountable number of possible values.

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} Find the probability that a student will take more than 60 minutes to finish the test.

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 probability density function for this uniform distribution?

If X has an exponential distribution,then f(x)approaches ____________________ as x approaches infinity.

Use the X² table to find the following values of X². a. b. c. d.

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

A random variable with density function e−x for x ≥ 0 has an exponential distribution whose mean is ____________________.

Which of the following is true about f(x)when X has a uniform distribution over the interval [a,b]?

Phone Orders The L.L.Bean catalog department that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product.The length of time was found to be a random variable best approximated by an exponential distribution with a mean equal to 3 minutes. -{Phone Orders Narrative} What proportion of customers having to hold more than 1.5 minutes will hang up before placing an order?

The y-intercept of the density function for an exponential distribution with parameter 10 is ____________________.

Light Bulb Lifetime The lifetime of a light bulb (in hours)is exponentially distributed with λ = 0.008. ​ ​ -{Light Bulb Lifetime Narrative} What is the mean and standard deviation of the light bulb's lifetime?

Diet Researchers studying the effects of a new diet found that the weight loss over a one-month period by those on the diet was normally distributed with a mean of 10 pounds and a standard deviation of 5 pounds. ​ ​ -{Diet Narrative} What proportion of the dieters lost more than 12 pounds?

A random variable X has a normal distribution with mean 132 and variance 36.If x = 120,its corresponding value of Z is 2.0.

If then the number of degrees of freedom v is:

Let X be a normally distributed random variable with a mean of 12 and a standard deviation of 1.5.What proportions of the values of X are: a.less than 14 b.more than 8 c.between 10 and 13

Phone Orders The L.L.Bean catalog department that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product.The length of time was found to be a random variable best approximated by an exponential distribution with a mean equal to 3 minutes. -{Phone Orders Narrative} Find the waiting time at which only 10% of the customers will continue to hold.

Use the t-table to find the following probabilities. a.P(t₈ > 2.306) b.P(t₈₀ > 2.639) c.P(t₂₄ > 1.711) d.P(t₃₅ > 1.306)

Suppose X is a normal random variable with mean 70 and standard deviation 3.Then P(X = 3)= ____________________.