In an experiment on the behavior of young children, each child is placed in an area with five toys. The response of interest is the number of toys that the child plays with.Past experiments with many subjects have shown that the probability distribution of the number of toys played with is as follows: Number of toys      0       1        2    3 Probability              0.05 0.20 0.44 0.31 Assume we sample a young child at random and let X be the number of toys this child plays with. (a) What is the expected value of X?  (b) What is the variance of X?  (c) What is the standard deviation of X?

The following report is from the National Highway Safety Administration, and it is based on over 800,000 deaths. The report lists the type of crash and the percent of fatalities: Type of Crash                                                          Percent of Fatalities Single car crash                                                       45% Two-car crash                                                         22% Car crashing with a truck                                         25% Crash involving 3 or more vehicles                           8% Consider a recent car crash that resulted in a fatality. What is the probability that a single car crash had occurred?

The following table shows the distribution of murders by type of weapon for murder cases in a particular country over the past 12 years. Complete parts (a) through (e). (b) What is the probability that a randomly selected murder resulted from a rifle or shotgun? (Type a decimal rounded to three decimal places as needed.) P(rifle or shotgun) = Interpret this probability. Select the correct choice below and fill in the answer box to complete your choice. OA. If 1000 murders were randomly selected, exactly of them would have resulted from a rifle or shotgun. B. If 1000 murders were randomly selected, we would expect about of the to have resulted from a rifle or shoto (c) What is the probability that a randomly selected murder resulted from a handgun, rifle, or shotgun? P(handgun, rifle, or shotgun) = (Type a decimal rounded to three decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box to complete your choice. OA. If 1000 murders…

3. For each experiment, fill in the blank with the letter for the probability histogram that corresponds to the quantity indicated. Experiment 1: A gambling game has a 30% chance of winning $2 and a 70% chance of losing $1. We play the game 100 times and keep track of the net amount won or lost. Experiment 2: We flip a coin 40 times and keep track of the number of heads. 0.08 90'0 0.12 0.08 0.04 000 0 0 20 10 40 20 60 8 80 30 (a) 100 (c) (e) 40 0.00 0.012 0.008 1000 0000 -100 -50 -100 -50 0 0 50 T 50 (b) 100 150 200 30 (d) (f) 100 150 200