U.S. airlines average about 4.5 fatalities per month. (Statistical Abstract of the United States: 2012). Assume that the probability distribution for x, the number of fatalities per month, can be approximated by a Poisson probability distribution. a. What is the probability that no fatalities will occur during any given month? b. What is the probability that one fatality will occur during any given month? c. Find E(x) and the standard deviation of x.

Suppose the probability that a U.S. resident has traveled to Canada is 0.18, to Mexico is 0.09, and to both countries is 0.04. What's the probability that an American chosen at random has traveled to Canada but not Mexico?

Suppose the probability that a U.S. resident has traveled to Canada is 0.18, to Mexico is 0.09, and to both countries is 0.04. What's the probability that an American chosen at random has a) traveled to Canada but not Mexico? b) traveled to either Canada or Mexico? c) not traveled to either country?

If x is a binomial random variable, calculate

$$\mu , \sigma ^ { 2 } , \text { and } \sigma$$

for each of the following:

$$n = 25 , p = .5$$

If you receive , on the average 5 email messages per day, in how many days out of a 365-day year would expect to receive exactly 5 message? Fewer than 5? Exactly 10? More than 10? Just 1? None at all?

Let X be a binomial random variable with p = 0.2 and n = 20. Use the binomial table in Appendix A to determine the following probabilities. a. P(X ≤ 3) b. P(X > 10) c. P(X = 6) d. P(6 ≤ X ≤ 11)

Let X be a binomial random variable with p = 0.25 and n = 3. Determine the probability distribution of the random variable Y = X².

If x is a binomial random variable, compute p(x) for each of the following cases:

$$n = 4 , x = 2 , q = .4$$

For weather-related crises, Los Angeles County schools have historically been closed an average of three days each year. What is the likelihood that Los Angeles County schools will be closed for four days in the upcoming school year?

U.S. airlines average about 1.6 fatalities per month. (Statistical Abstract of the United States: 2010.) Assume the probability distribution for $Y$, the number of fatalities per month, can be approximated by a Poisson probability distribution.

a. What is the probability that no fatalities will occur during any given month?

b. What is the probability that one fatality will occur during any given month?

c. Find $E(Y)$ and the standard deviation of $Y$.

If x is a binomial random variable, compute p(x) for each of the following cases:

$$n = 5 , x = 1 , p = .2$$

A keyboard for a personal computer is known to have a mean life of 5 years. The life of the keyboard can be modeled using an exponential distribution. (a) What is the probability that a keyboard will have a life between 2 and 4 years? (b) What is the probability that the keyboard will still function after 1 year? (c) If a warranty is set at 6 months, what is the probability that a keyboard will need to replaced under warranty?

Airline fatalities. Over the past 5 years, U.S. airlines average about 1 fatality per month (U.S. Department of Transportation, National Transportation Statistics: 2015). Assume that the probability distribution for $x$, the number of fatalities per month, can be approximated by a Poisson probability distribution. What is the probability that no fatalities will occur during any given month?

The Journal of Visual Impairment & Blindness (May–June 1997) published a study of the lifestyles of visually impaired students. Using diaries, the students kept track of several variables, including number of hours of sleep obtained in a typical day. These visually impaired students had a mean of 9.06 hours and a standard deviation of 2.11 hours. Assume that the distribution of the number of hours of sleep for this group of students is approximately normal. a. Find the probability that a visually impaired student obtains less than 6 hours of sleep on a typical day. b. Find the probability that a visually impaired student gets between 8 and 10 hours of sleep on a typical day. c. Twenty percent of all visually impaired students obtain less than how many hours of sleep on a typical day?