Question

Please answer with method or formula used.

A) Puenaa is getting married tomorrow, at an outdoor ceremony in the desert. In recent years, it has rained only 5 days each year. Unfortunately, the weatherman has predicted rain for tomorrow. When it actually rains, the weatherman correctly forecasts rain 90% of the time. When it doesn't rain, he incorrectly forecasts rain 10% of the time. What is the probability that it will rain on the day of Puenaa's wedding?

B) A randomly selected vehicle has a 10% chance of failing inspection. A simple random
sample of 12 vehicles is selected. a) What is the mean and standard deviation number of vehicles in the sample that fail? b) What is the probability that at least 1 vehicle fails? c) What is the probability that at least 3 vehicles fail?

C) An urn contains 15 marbles and exactly 6 of them are red, and the rest are blue. Suppose I choose 4 marbles, one after the other and without replacement. a) What is the probability I observe this specific sequence: RRBR b) What is the probability exactly 3 marbles are red? c) What is the probability 3 or more are red?

D) On a quiz, the mean quiz score was 7.7 and the median is 7. The first quartile is 3.5 and the third quartile is 9. The maximum and minimum scores are 10 and 0 respectively. The standard deviation of scores is 1.5. There are 40 students in the class
a) Suppose four students with zeros had their scores changed to 1. Does this effect the mean? How? Does this effect the median? How?
b) Suppose now that instead of what was done in part (a), every student had one point added to their score. How does this effect the mean? The median? The standard deviation?
c) Find the 5% trimmed mean if you know that the top four scores are 10,10,9,9 and the bottom four scores are 0,1,1,2

E) Imagine that you encounter three traffic lights in a row as you pass through three intersections. The event GGG means that you did not have to stop at any of the lights. The event GSG means that you had to stop only at the second light.
a) list all 8 outcomes of this sample space b) list the outcomes for the event of stopping at exactly one light c) If the lights operate independently, and you have a 0.3 probability of stopping at any one of the lights, find the probability that, in passing though the three intersections, you have to stop at exactly one light
d) Suppose now the lights are not independent. Now assume that if you are stopped at one light, the probability you have to stop at the next light is 0.1, and that if you pass through one light, the probability you have to stop at the next light is 0.4. Assume also that the first light you encounter has a .30 probability of stopping you. Compute the probability that, in passing the through the three intersections, you stop at exactly one light.

Answer 1