Airlines sometimes overbook flights. Suppose that for a plane with 50 seats, 55 passengers have tickets. Define the randor variable Y as the number of ticketed passengers who actually show up for the flight. The probability mass function of Y appears in the accompanying table. 45 46 47 48 49 50 51 52 53 54 55 P(Y) 0.05 0.10 0.12 0.14 0.25 0.17 0.03 0.06 0.05 0.02 0.01 Calculate V(Y) and oy. (Round your variance to four decimal places and your standard deviation to two decimal places.) V(Y) Oy = Determine the probability that Y is within 1 standard deviation of its mean value.

A census collected data on everyone that lived in a certain small town. The random variable X is the number of girls born to a randomly selected couple in that town who has four children. Its probability distribution is shown below. Complete parts a through c. X 4 O 0 P(X=x) 0.0857 2 0.3208 3 0.2415 0.2447 0.1073 i ne mean number of children in a family with four girls iS b. Obtain the standard deviation of the random variable. 0= 1.1209 (Round to four decimal places as needed.) c. Construct a probability histogram for the random variable; locate the mean; and show one-, two-, and three-standard-deviation intervals. Choose the correct histogram below. B. O C. D. Number of Girls Number of Girls Number of Girls Number of Girls 0.5- 0.5- 0.4- 0.3- 0.4- 0.5- 0.4- 0.3- 0.2- 0.1- 0.3- 0.2- 0.2- n 0.1- 0.1- 0 0012 0 1 2 3 4 01234 01234 01234 The mean is 2.0400. (Type an integer or decimal rounded to four decimal places as needed.) The one-standard-deviation interval is.. the…

Let X = {Email, In Person, Instant Message, Text Message}; P(Email) = 0.06 P(In Person) = 0.55 P(Instant Message) = 0.24 P(Text Message) = 0.15   Is this model a probability distribution? A. Yes. B. No. C. Maybe.

Fill in the P(X=x) values to give a legitimate probability distribution for the discrete random variable X, whose possible values are 2, 2, 4, 5, and 6. Value x of X P(x x) -2 0.16 4 0.11 0.17 6