Exam 5: Continuous Random Variables

The lifetime of a stereo component is exponentially distributed with mean 1,000 days. What is the probability that the lifetime: -Is greater than or equal to 700 days?

The standard deviation of a standard normal distribution is always equal to _____.

The fill weight of a certain brand of adult cereal is normally distributed with a mean of 910 grams and a standard deviation of 5 grams. -If we select one box of cereal at random from this population,what is the probability that it will weigh less than 900 grams?

At a Great Lakes nuclear power plant, lake water is used as part of the cooling system. This raises the temperature of the water that is discharged back into the lake. The amount that the water temperature is raised has a uniform distribution over the interval from 10 to 25º C. -What is the expected value of the temperature increase?

For a continuous distribution,the probability that the random variable of interest assumes a one specific value is zero.

A plant manager knows that the number of boxes of supplies received weekly is normally distributed with a mean of 200 and a standard of 20. -What percentage of the time will the number of boxes received weekly be between 180 and 210?

The z value tells us the number of standard deviations that a value x is from the mean.

The fill weight of a certain brand of adult cereal is normally distributed with a mean of 910 grams and a standard deviation of 5 grams. -If we select one box of cereal at random from this population,what is the probability that it will weigh more than 904 grams?

__________ values of the standard deviation results in a normal curve that is wider and flatter.

Consider a normal population with a mean of 10 and a standard deviation 2. -Find P(X ≥ 10).

A company must decide their contribution to their pension plan based on the probability distribution of the length of life of their retired employees.Suppose the probability distribution of the lifetimes of their employees is approximately a normal distribution with μ = 74 years and σ = 8.6 years.What percentage of their retired employees would receive payments: -Beyond age 76

A paint sprayer coats a metal surface with a layer of paint between 0.43 and 1.23 millimeters thick. The thickness of the coat of paint is approximately uniformly distributed. -What are the mean and standard deviation of the thickness of the coat of paint on the metal surface?

What is the probability that a random variable having a standard normal distribution is between .87 and 1.28?

Consider a normal population with a mean of 10 and a standard deviation 2. -Find P(X > 13).

Which one of the following variables could be modeled using a continuous probability distribution?

The mean of a standard normal distribution is always equal to _______.

A paint sprayer coats a metal surface with a layer of paint between 0.43 and 1.23 millimeters thick. The thickness of the coat of paint is approximately uniformly distributed. -What is the probability that paint from this sprayer on any given metal surface will be between 0.75 and 1.05 millimeters thick?

The probability that an appliance is in repair is .5.If an apartment complex has 100 such appliances,what is the probability that at least 60 will be in repair? Use the normal approximation to the binomial.

The normal probability distribution is a discrete probability distribution.

Find z when the area to the left of z is .05