Name and section: 1. (10 points) A box contains 5 black balls and 4 red balls. (a) If a ball is selected at random from the box, what is the probability it is red? (b) If two balls are selected (without replacement) what is the probability that they are both red? (c) If three balls are selected at random (without replacement) what is the probability that at least one of the balls is red?. 2. (5 points) Determine whether the given distribution represents a probability distribution (pdf). If it doesn't give a reason why it does not. X 20 30 40 50 (a) P(x) NIH X -2 -3 -4 -5 ( b ) P(x) NIH AIH 0014 3. (10 points) The probability that a hockey team scores 1 goal in a game is 0.124, the probability that a hockey team scores 2 goals is 0.197, the probability that a hockey team scores 3 goals is 0.302, 4 goals is 0.094, 5 goals is 0.083 and 0 goals is 0.200. Let X be the random variable which is the number of goals scored by the hockey team . (a) Construct the probability disribution for X and draw the graph. (b) Compute the mean of X, UX = and the standard deviation of X, ox = (c) What is the expected number of goals that the hockey team would score? (d) What is the probability that the hockey team scores at least 2 goals?4. (10 points) The county department recorded the following probabilities for the numbe of accidents per day for a certain 'echLY- Number of accidents 3: D 1 2 a 4 Probability P x 0.4 0.2 0.2 0.1 0.1 (5) Compute the mean, the val-lance. and the standard deviation of X ux ='n73; =WX = (b) Compute Prob(X > 2) =__, Prob(X 1.25) = and 70% of the area under the standard normal curve lies to the left of z = 9, (10 points) The average length of a hospital stay for diagnoses is 3.8 days. If we assume that the lengths are normally distributed with a standard deviation of 1.75 days, then answer the following questions. Let X=number of days stay in the hospital for diagnoses. (a) What is Prob(X > 5)? _ (b) What is Prob(2 5)? _ (b) What is Prob(2 BY (b) What is Prob(