3. An airline company accepts 100 reservations for a flight that has 72 available seats. A per- son booking a reservation does not show up in the flight with probability q = 0.1. Using Chebyshev's inequality, find an upper bound in the probability that no traveler showing up is bumped (excluded) from the flight (if Y is the total number of people showing for the flight, we are interested in an upper bound for P(Y <72)).

The probabihity of winning a prize in a game of chance is 0.48. What is the least number of games that must be played to ensure that the probability of winning at le ast twice is more than 0.95?

The graph of the discrete probability to the right represents the number of live births by a mother 49 to 53 years old who had a live birth in 2015. Complete parts (a) through (d) below. 0 1 (a) What is the probability that a randomly selected 49- to 53-year-old mother who had a live birth in 2015 has had her fourth live birth in that year? (Type an integer or a decimal.) (b) What is the probability that a randomly selected 49- to 53-year-old mother who had a live birth in 2015 has had her fourth or fifth live birth in that year? (Type an integer or a decimal.) (c) What is the probability that a randomly selected 49- to 53-year-old mother who had a live birth in 2015 has had her sixth or more live birth in that year? (Type an integer or a decimal.) Statcrunch no JL @ 1 # с $ % JI JU & 0.30 0.25 0.20 0.15 0.10 0.05- 0.00 U 165 0.112 0.094 Number of Live Births 7 R # 8 A G

2) A data packet consists of 10,000 bits, where each bit is a 0 or a 1 with equal probability. Estimate the probability of having at least 5200 ones in terms of the Q-function. Show your work.

Please solv within 30min (a) 0.1008 0.0010 0.8008 0.3193 (b) 0.1008 0.0010 0.8008 0.3193

3. The amount of weight it takes to break a piece of string is normally distributed with u-22 pounds and 4 pounds. You put a weight of 18 pounds on the string. What is the probability that the string breaks? In other words, what is the probability that the weight needed to break the string is less than or equal to 18 pounds? (Hint: This is asking for Prob(-∞o << 18), which can be transformed into an inequality for z. Now think what (a) measures. You might wonder whether <0 should be included. When this is changed to z, we are looking at z <-5.5, which is negligible. See the Technical Point in the section on the normal distribution.) (Give your answer as a decimal rounded to 4 decimal places.) 0.8413 I Output: R