Exam 7: Continuous Probability Distributions

Let X = the time (in minutes) that a postal clerk spends with her customers.This time is known to have an exponential distribution with an average of 4 minutes.What is the variance for this distribution?

The amount of time a person waits for a cab in Manhattan is uniformly distributed.If the maximum time a person waits for a cab in Manhattan is 5 minutes and the minimum is 30 seconds, what is the average wait time for a cab in Manhattan?

Although the binomial distribution is discrete, in many cases it can be modeled using a normal distribution.If X is binomial with mean = μx and standard deviation = σx, then we can define a new random variable Y that is normal with the same mean and same standard deviation.In this case under certain assumptions,P(X ≤ x) ≈ P(Y ≤ x).This relationship is most useful when X has a large number of trials.If X is binomial with a mean of 25 and a standard deviation of 4.33 (n = 100, p = 0.25), what is P(X ≤ 23) using the normal approximation discussed here?

The plots shown here are normal probability plots for random samples of 65 healthy male and 65 healthy female body temperatures. Which group is more likely to be normally distributed?

Let X = the time (in minutes) that a postal clerk spends with her customers.This time is known to have an exponential distribution with an average of 4 minutes.What is the probability that the clerk spends 4 to 5 minutes with a randomly selected customer?

The maximum value for any cumulative probability distribution function is always

Quality control engineers create acceptable boundaries for variability within the processes they monitor.They determine that the acceptable boundary for a certain heat exchange process at a gasoline refinery must be set such that under normal operating conditions the threshold would be exceeded only 1% of the time.Under normal operating conditions, the process varies according to a normal distribution, with mean temperature of 231°C and standard deviation of 2.5°C.What upper temperature should they set so that the process will normally exceed the temperature 0.51% of the time?

X follows a normal distribution with a mean of 1112.5 and a variance of 144.2.Standardize an X value of 1000.

The higher the peak of a normal distribution,

Metro buses are scheduled to arrive at each stop every 30 minutes.If the time a person waits at a bus stop is uniformly distributed and the maximum possible wait time for a bus is 30 minutes, what is the probability that you will wait more than 25 minutes for a bus?

Suppose the cumulative distribution function (CDF) of continuous random variable X is defined as follows: where 1 ≤ x < ∞.What is P(1.5 ≤ X ≤ 2)?

Assume that the lifetime (in hours) of a particular car fan can be modeled with an exponential distribution with parameter 0.0003.Find the proportion of fans that will last for at least 10,000 hours.

The speed at which an automated assembly line produces a product follows a normal distribution, with a mean production time of 32.20 seconds and a standard deviation of 1.05 seconds.What is the probability that a product requires more than 34 seconds to produce?

A major producer of incandescent light bulbs wishes to model the amount of time incandescent bulbs manufactured at a specific plant will last.The company uses an exponential random variable to model bulb life.If random variable X, which represents the lifetime of these incandescent bulbs, is exponentially distributed with λ = 0.0012 (corresponding to measurements in hours), what is the modeled mean lifetime of these bulbs?

Let X be a continuous random variable and let c be a constant.Which of the following statements is true?

The smiling times (in seconds) of an 8-week-old baby can be modeled with a uniform distribution with a = 0 and b = 23 seconds.What is the probability that a randomly chosen 8-week-old baby smiles between 2 and 18 seconds?

Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 C3 150 0 69.912 0.0798 0.977 67.625 69.175 69.948 Variable Maximum C3 72.339 If the data set presented here were normal, which value would most likely fall into the third quartile?

If the heights of NBA players are normally distributed with a mean height of 73.5 inches and a standard deviation of 2.2 inches, what is the probability of randomly selecting an NBA player who is between 72 and 73 inches tall?

A study of college dropouts models the number of undergraduate credits a student successfully earns prior to quitting using an exponential random variable.If the observed average number of credits earned is 22.5, what proportion of students drop out with more than 100 credits, assuming an exponential random variable is appropriate here?

X is a normally distributed random variable with μx = 125 and σx = 12.5.What is P(X ≥ 110)?