Exam 7: Random Variables and Discrete Probability Distributions

Suppose that customers arrive at a drive-through window at an average rate of three customers per minute and that their arrival follows the Poisson model. A) Write the probability density function of the distribution of the time that will elapse before the next customer arrives. B) Use the appropriate exponential distribution to find the probability that the next customer will arrive within 1.5 minutes. C) Use the appropriate exponential distribution to find the probability that the next customer will not arrive within the next 2 minutes. D) Use the appropriate Poisson distribution to answer part (c).

The expected number of heads in 90 tosses of an unbiased coin is: A. 30. B. 45. C. 50. D. 60.

Given that X is a binomial random variable, the binomial probability P(X $\geq$ x) is approximated by the area under a normal curve to the right of: A. x-0.5 B. x+0.5 C. x-1. D. x+1

An official from the Australian Securities and Investments Commission estimates that 75% of all investment bankers have profited from the use of insider information. If 15 investment bankers are selected at random from the Commission's registry, find the probability that: a. at most 10 have profited from insider information. b. at least six have profited from insider information. c. all 15 have profited from insider information.

A Bernoulli trial is where each trial of an experiment has four possible outcomes, the probability of success is p and the trials are not independent.

Given a binomial random variable with n =15 and p = 0.40, find the exact probabilities of the following events and their normal approximations. a. X = 6. b. X $\geq$ 9. c. X $\leq$ 10.

Gender is an example of a continuous random variable.

A discrete random variable can take either finite or infinite values as long as the values are countable.

Historical data collected at the Commonwealth Bank in Sydney revealed that 80% of all customers applying for a loan are accepted. Suppose that 50 new loan applications are selected at random. a. Find the expected value and the standard deviation of the number of loans that will be accepted by the bank. b. What is the probability that at least 42 loans will be accepted? c. What is the probability that the number of loans rejected is between 10 and 15, inclusive?

The number of accidents that occur annually on a busy stretch of highway is an example of: A a discrete random variable. B a continuous random variable. C a discrete probability distribution. D a continuous probability distribution.

An advertising executive receives an average of 10 telephone calls each afternoon between 2 and 4pm. The calls occur randomly and independently of one another. a. Find the probability that the executive will receive 13 calls between 2 and 4pm on a particular afternoon. b. Find the probability that the executive will receive seven calls between 2 and 3pm on a particular afternoon. c. Find the probability that the executive will receive at least five calls between 2 and 4pm on a particular afternoon.

The lottery commission has designed a new instant lottery game. Players pay $1.00 to scratch a ticket, where the prize won, X, (measured in $) has the following discrete probability distribution : X P[X] 0 0.95 10 0.049 100 0.001 Which of the following best describes the standard deviation of X ? A 14.552 in B 3.815 in \ C 0.348 in \ D None of these choices are correct

The following table is a valid probability distribution, for a random variable X, where the individual probabilities are unknown. X P[X] -3 -2 0 1 2 Which of the following statements is correct ? \begin{array}{|l|l|}\hline A&\text {The expected value of \mathrm{X} can only be 0 . }\\\hline B&\text { The expected value of \( \mathrm{X} \) could be 3 .}\\\hline C&\text { The expected value of \( \mathrm{X} \) could be 0.5}\\\hline D&\text {None of these choices are correct }\\\hline \end{array}

Which of the following is not a characteristic of a binomial experiment? A There is a sequence of identical trials. B Each trial results in two or more outcomes. C The trials are independent of each other. D Frobability of success p is the same from one trial to another.

A binomial distribution for which the number of trials n is large can well be approximated by a Poisson distribution when the probability of success, p, is: A larger than 0.95 B larger than 0.50 C between 0.25 and 0.50 . D smaller than 0.05