Exam 6: Random Variables and Discrete Probability Distributions

For a random variable X, if V(cX) = 4V(X), where V refers to the variance, then c must be 2.

On the average, 1.6 customers per minute arrive at any one of the checkout counters of Sunshine food market. What type of probability distribution can be used to find out the probability that there will be no customers arriving at a checkout counter in 10 minutes?

Stress: Consider a binomial random variable X with n = 5 and p = 0. 40, where X represents the number of times in the final exam week a student with 18 credit hours may feel stressed. -Find P(X < 3).

A binomial experiment consists of a(n) ____________________ number of trials, n.

A lab at the DeBakey Institute orders 150 rats a week for each of the 52 weeks in the year for experiments that the lab conducts. Suppose the mean cost of rats used in lab experiments turned out to be $20.00 per week. Interpret this value.

For a random variable X, V(X + 3) = V(X + 6), where V refers to the variance.

Classified Department Phone Calls: A classified department receives an average of 10 telephone calls each afternoon between 2 and 4 P.M. The calls occur randomly and independently of one another. -Find the probability that the department will receive at least five calls between 2 and 4 P.M. on a particular afternoon.

The number of accidents that occur at a busy intersection in one month is an example of a Poisson random variable.

The possible values of a Poisson random variable start at ____________________.

The ____________________ of a Poisson distribution is the rate at which successes occur for a given period of time or interval of space.

Classified Department Phone Calls: A classified department receives an average of 10 telephone calls each afternoon between 2 and 4 P.M. The calls occur randomly and independently of one another. -Find the probability that the department will receive seven calls between 2 and 3 P.M. on a particular afternoon.

Montana Highways: A recent survey in Montana revealed that 60% of the vehicles traveling on highways, where speed limits are posted at 70 miles per hour, were exceeding the limit. Suppose you randomly record the speeds of ten vehicles traveling on US 131 where the speed limit is 70 miles per hour. Let X denote the number of vehicles that were exceeding the limit. -Find P(4 < X < 9).

The probability of a success in a binomial experiment is denoted by ____________________.

Another name for the mean of a probability distribution is its expected value.

Shopping Outlet: A shopping outlet estimates the probability distribution of the number of stores shoppers actually enter as shown in the table below. -Use the laws of expected value to calculate the mean of Y from the probability distribution of X.

A(n) ____________________ random variable is one whose values are uncountable.

Unsafe Levels of Radioactivity: The number of incidents at a nuclear power plant has a Poisson distribution with a mean of 6 incidents per year. -Find the probability that there will be exactly 3 incidents in a year.

In a Poisson experiment, the number of successes that occur in any interval of time is ____________________ of the number of success that occur in any other interval.

Shopping Outlet: A shopping outlet estimates the probability distribution of the number of stores shoppers actually enter as shown in the table below. -Find the variance and standard deviation of the number of stores entered.

The standard deviation of a binomial random variable X is given by the formula $\sigma$ ² = np(1 -p), where n is the number of trials, and p is the probability of success.