Answer the following questions relating to probability, distributions, and sampling distributions. For most of the questions, you will need to use R to determine the answer. Where relevant, round your answers to FOUR decimal places.

1. P(X1.9168)P(X1.9168) for XN(0,1)XN(0,1) answer
2. P(X81.5701)P(X81.5701) for XN(77,15.4)XN(77,15.4) Answer
3. P(7.0335X7.0335)P(7.0335X7.0335) for XN(0,9)XN(0,9) Answer
4. P(8.0335X7.0335)P(8.0335X7.0335) for XN(0,9)XN(0,9) Answer
5. P(X1.898)+P(X1.898)P(X1.898)+P(X1.898) for XN(0,1)XN(0,1) Answer
6. Suppose that XN(77,15.4)XN(77,15.4). For some value xx, we have that P(Xx)=0.3969P(Xx)=0.3969. What must be the value of xx? Answer
7. Suppose it is claimed that amongst the population of human adults, the number of hours spent sleeping per day is normally distributed with a mean of =7=7 and variance of 2=1.12=1.1. Further suppose that we wish to study the mean of the population by taking a random sample of n=45n=45 adults. Using this information, write down the distribution of the sample mean, XX. Note: In each box, enter a single number rounded to four decimal places where relevant. XN(XN( Answer ,, Answer ))
8. Following on from the previous question, what is the probability that when we take a random sample of n=45n=45 adults, the sample mean would be greater than 7.1562? Answer
9. Again following on from the previous question, what is the probability that when we take a random sample of n=45n=45 adults, the sample mean would be either greater than 7.1562 or less than 6.8438? Answer
10. Suppose a random sample of n=22n=22 is taken from a population with an unknown distribution that has =7=7 and 2=1.048822=1.04882. What is the distribution of XX? XX AnswerN(7, 1.0488)N(7, 1.1)N(7, 0.2236)N(7, 05)The distribution is unknown

For the remainder of this question, we will consider one of the world's most popular video games, Minecraft (adapted from Mills & Mills, 2016). In this game, the character (you) can attempt to tame a wolf with a bone. Assume that you get 7 tries to tame the wolf, i.e.there are 7 bones. Each time you tame the wolf, the wolf becomes a dog and a new wolf appears which you can then attempt to also tame. This continues until you have used up all 7 bones, and the goal is to end up with as many dogs as possible at the end of the game. The probability of taming the wolf with each attempt is fixed at 0.4. Let XX denote the number of dogs at the end of the game so that XBIN(7,0.4)XBIN(7,0.4). Assume you are about to play the game.

1. What is the probability you will tame exactly 3 dogs? Answer
2. What is the probability you will tame less than 4 dogs? Answer
3. What is the probability you will tame more than 4 dogs? Answer
4. If you tame more than half of the dogs, you win. Otherwise, you lose. What is the probability you will win the game? Answer
5. The probability that you will tame some number xx or less dogs is 0.710208. What must xx be (round to the nearest whole number)? Answer