Exam 5: Continuous Random Variables

The time between equipment failures (in days)at a particular factory is exponentially distributed with a mean of 4.5 days. A machine just failed and was repaired today. a. Find the probability that another machine will fail within the next day. b. Find the probability that there will be no more equipment failures in the next week.

Suppose that $x$ has an exponential distribution with $\theta = 1.5$ . Find $P ( x > 1 )$ .

Suppose x is a random variable best described by a uniform probability distribution with c = 20 and $\mathrm { d } = 40 . \text { Find } \mathrm { P } ( 32 \leq \mathrm { x } \leq 40 ) \text {. }$

The time between customer arrivals at a furniture store has an approximate exponential distribution with mean θ = 8.5 minutes. If a customer just arrived, find the probability that the next Customer will not arrive for at least 20 minutes.

The time (in years)until the first critical-part failure for a certain car is exponentially distributed with a mean of 3.4 years. Find the probability that the time until the first critical-part failure is less Than 1 year.

The time between customer arrivals at a furniture store has an approximate exponential distribution with mean θ = 8.5 minutes. If a customer just arrived, find the probability that the next Customer will arrive in the next 5 minutes.

A machine is set to pump cleanser into a process at the rate of 6 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the Uniform distribution over the interval 5.5 to 8.5 gallons per minute. What is the probability that at The time the machine is checked it is pumping more than 7.0 gallons per minute?

Assume that x is a binomial random variable with n = 100 and p = 0.60. Use a normal approximation to find P(x < 48).

A certain baseball player hits a home run in 4% of his at-bats. Consider his at-bats as independent events. How many home runs do we expect the baseball player to hit in 650 at-bats?

The exponential distribution is governed by two quantities, μ and σ, that determine its shape and location

The price of a gallon of milk follows a normal distribution with a mean of $3.20 and a standard deviation of $0.10. What proportion of the milk vendors had prices that were less than $3.075 per Gallon?

When the points on a normal probability plot lie approximately on a straight line, the data are approximately normally distributed.

Assume that x is a binomial random variable with n = 400 and p = 0.30. Use a normal approximation to find P(x > 100).

The diameters of ball bearings produced in a manufacturing process can be described using a uniform distribution over the interval 6.5 to 8.5 millimeters. What is the probability that a Randomly selected ball bearing has a diameter greater than 7.4 millimeters?

Suppose x is a random variable best described by a uniform probability distribution with c = 20 and $d = 40 . \text { Find } P ( x > 40 )$

Transportation officials tell us that 80% of drivers wear seat belts while driving. What is the probability that between 656 and 665 drivers in a sample of 850 drivers wear seat belts?

Suppose x is a random variable best described by a uniform probability distribution with c = 30 and $d = 110 . \text { Find } P ( x < 46 )$

The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 1900 miles. What is the Probability a certain tire of this brand will last between 56,010 miles and 56,580 miles?

The exponential distribution has the property that its mean equals its standard deviation.

The age of customers at a local hardware store follows a uniform distribution over the interval from 18 to 60 years old. Find the average age of customers to this hardware store.