Exam 5: Continuous Random Variables

Suppose x is a uniform random variable with c = 40 and d = 70. Find the standard deviation of x. A) $\sigma = 8.66$ B) $\sigma = 31.75$ C) $\sigma = 1.58$ D) $\sigma = 3.03$

IQ test scores are normally distributed with a mean of 96 and a standard deviation of 12. An individual's IQ score is found to be 110. Find the z-score corresponding to this value.

The probability density function for an exponential random variable x has a graph called a bell curve.

Assume that x is a binomial random variable with n = 400 and p = 0.30. Use a normal approximation to find P(x ≥ 110).

A machine is set to pump cleanser into a process at the rate of 7 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 6.5 to 9.5 gallons per minute. What is the probability that at the time the machine is checked it is pumping more than 8.0 gallons per minute?

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?

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 study of college students stated that 25% of all college students have at least one tattoo. In a random sample of 80 college students, let x be the number of the students that have at least one tattoo. Find the mean and standard deviation for this binomial distribution.

Suppose that the random variable x has an exponential distribution with θ = 1.5. Find the mean and standard deviation of x.

Before a new phone system was installed, the amount a company spent on personal calls followed a normal distribution with an average of $700 per month and a standard deviation of $50 per month. Refer to such expenses as PCE's (personal call expenses). Find the probability that a randomly selected month had PCE's below $550.

The volume of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of 12.54 ounces and a standard deviation of 0.36 ounce. The company receives complaints from consumers who actually measure the amount of soda in the cans and claim that the volume is less than the advertised 12 ounces. What proportion of the soda cans contain less than the advertised 12 ounces of soda?

The mean of the standard normal distribution is 1 and the standard deviation is 0.

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.

Transportation officials tell us that 80% of drivers wear seat belts while driving. What is the probability of observing 633 or fewer drivers wearing seat belts in a sample of 850 drivers?

A study of college students stated that 25% of all college students have at least one tattoo. In a random sample of 80 college students, let x be the number of the students that have at least one tattoo. Find the approximate probability that more than 30 of the sampled students had at least one tattoo.

The diameters of ball bearings produced in a manufacturing process can be described using a uniform distribution over the interval 2.5 to 8.5 millimeters. What is the probability of a randomly selected ball bearing having a diameter less than 4.5 millimeters?

Determine if it is appropriate to use the normal distribution to approximate a binomial distribution when n = 7 and p = 0.3.

A certain baseball player hits a home run in 3% of his at-bats. Consider his at-bats as independent events. How many home runs do we expect the baseball player to hit in 600 at-bats?

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?

Nearly 100% of the observed occurrences of a random variable x that is normally distributed will fall within three standard deviations of the mean of the distribution of x.