On a popular app, users rate restaurants as 1. 2. 3. 4, or 5 stars. Suppose a rating is randomly se ected from all the ratings on the app. Let X be the number of stars of the selected rating, Here is the probability distribution of X Value x of X P(X=x) For parts (a) and (b) below. Find the probability that the randomly selected restaurant rating has the described number of stars. (a) 3 or more: (b) Fewer than 4: 0.21 0.20 0.11 0.24 0.24

Make a histogram of the probability distribution of X. Describe its shape.

Suppose we played roulette x5 times (where x = 3 is the last digit of your student ID) and each time we bet on the number 17. In each game, xthe probability of winning is 1/37. Calculate the probability P(X = z), where z is the second-to-last digit of your student ID (in this case, z = 5). Draw the probability distribution function graph for the given scenario. Also, calculate the probability of winning less than 5 timesDo this task in R commander.

The proportion of eligible voters in the next election who will vote for the incumbent is assumed to be 53.5%. What is the probability that in a random sample of 440 voters, less than 48.3% say they will vote for the incumbent? Probability =

Gg.94.   According to Baseball Insider Magazine 25% of major league pitchers are left-handed. A recent report shows that 60% of left-handed pitcher undergo rotator cuff surgery, while 30% of right-handed pitchers undergo rotator cuff surgery. If a major league pitcher underwent rotator cuff surgery yesterday afternoon, what is the probability that this pitcher was right-handed and underwent rotator cuff surgery?