Exam 5: Continuous Random Variables

Suppose that 67% of the employees of a company participate in the companyʹs medical savings program. Let x be the number of employees who participate in the program in a random sample of 50 employees. Find the mean and standard deviation of x.

The time between arrivals at an ATM machine follows an exponential distribution with θ = 10 minutes. Find the probability that more than 25 minutes will pass between arrivals.

Suppose x is a uniform random variable with c = 10 and $\mathrm { d } = 80 . \text { Find } \mathrm { P } ( \mathrm { x } > 52 )$

Transportation officials tell us that 90% of drivers wear seat belts while driving. What is the probability of observing 511 or fewer drivers wearing seat belts in a sample of 600 drivers?

Find a value of the standard normal random variable $z$ , called $z _ { 0 }$ , such that $\mathrm { P } \left( z \geq z _ { 0 } \right) = 0.70$ .

The waiting time (in minutes)between ordering and receiving your meal at a certain restaurant is exponentially distributed with a mean of 10 minutes. The restaurant has a policy that your meal is Free if you have to wait more than 25 minutes after ordering. What is the probability of receiving a Free meal?

High temperatures in a certain city for the month of August follow a uniform distribution over the interval 75°F to 95°F. What is the probability that a random day in August has a high temperature that exceeds 80°F?

Which shape is used to represent areas for a normal distribution?

A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a Mean of 460 seconds and a standard deviation of 50 seconds. Between what times do we expect Approximately 95% of the boys to run the mile?

Use the standard normal distribution to find $\mathrm { P } ( \mathrm { z } < - 2.33 \text { or } z > 2.33 )$

Suppose that the random variable x has an exponential distribution with θ = 3. a. Find the probability that $x$ assumes a value more than three standard deviations from $\mu$ . b. Find the probability that $x$ assumes a value less than one standard deviation from $\mu$ . c. Find the probability that $x$ assumes a value within a half standard deviation of $\mu$ .

The total area under a probability distribution equals 1.

For a standard normal random variable, find the probability that z exceeds the value -1.65.

The diameters of ball bearings produced in a manufacturing process can be described using a uniform distribution over the interval 4.5 to 9.5 millimeters. What is the probability of a randomly selected ball bearing having a diameter less than 6.5 millimeters?

The amount of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of 12.45 ounces and a standard deviation of 0.30 ounce. Each can holds a Maximum of 12.75 ounces of soda. Every can that has more than 12.75 ounces of soda poured into It causes a spill and the can must go through a special cleaning process before it can be sold. What Is the probability that a randomly selected can will need to go through this process?

Suppose x is a random variable best described by a uniform probability distribution with c = 100 and $\mathrm { d } = 40 . \text { Find } \mathrm { P } ( \mathrm { x } \geq 100 )$

A loan officer has 74 loan applications to screen during the next week. If past record indicates that she turns down 19% of the applicants, what is the z-value associated with 69 or more of the 74 applications being rejected?

A machine is set to pump cleanser into a process at the rate of 4 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 3.5 to 4.5 gallons per minute. Find the probability that the machine pumps less than 3.75 gallons during a randomly selected minute.

Suppose a random variable $x$ is best described by a normal distribution with $\mu = 60$ and $\sigma = 9$ . Find the $z$ -score that corresponds to the value $x = 60$ .