I’m working on a probability exercise and need guidance to help me understand better.Question
1. Use Normal approximation to estimate the probability of getting less than 51 tails in 100 fair coin tosses.Question
2. A fair coin is to be flipped 26 times, what is the probability of predicting at least 21 out of 26 of the outcomes correctly?Question
3. The bus is meant to arrive at 8am every morning but it is regularly late. The amount of time the bus is late (in minutes) is a continuous Uniform random variable between 1 and 15 minutes. ‘
Which of the following statements is true?A. The mean amount of time the bus is late is 8 minutesB. The standard deviation of the amount of time that the bus is late is about 4.04 minutes.C. It is less likely that the bus is late for more than 14 minutes than it is late for less than 2 minutesD. None of the aboveQuestion
4. Given the significance levels and the P-values for a hypothesis test, determine for each if the null hypothesis should be rejected.a) a=0.07, P=0.06b) a=0.06, P=0.001c) a=0.01, P=0.06Question
5.The time (in minutes) between arrivals of customers to a bank is modelled by the Exponential distribution with mean 0.52.a) What is the probability that the time between consecutive customers is less than 15 seconds?b) Find the probability that the time between consecutive customers is between 10 and 15 seconds.c) Given that the time between consecutive customers arriving is greater than 10 seconds, what is the chance that it is greater than 15 seconds?Question
6. Pradeep wants to determine a 90% confidence interval for the true proportion p of students in the local area who attend their home cricket matches. Out of n randomly selected people he finds exactly half attend their home cricket matches. How large would n have to be to get a margin of error less than 0.03 for p?Question
7. The number of burgers consumed per month by college students is normally distributed with a mean of 11 and a standard deviation of 3.a) What proportion of college students consume more than 12 burgers per month?b) What is the probability that in a random group of 8 students, a total of more than 80 burgers are consumed?Question
8. For 30 randomly selected soccer games, the mean gross broadcasting revenue is 2.01 million dollars.Part a) Assuming a population standard deviation gross revenue of 0.55 million dollars, obtain a 99% confidence interval for the mean gross revenue of all soccer matches (in millions).Part b) Which of the following is the correct interpretation for your answer in part (a)? A. There is a 99% chance that the mean gross revenue of all soccer matches lies in the intervalB. If we repeat the study many times, 99% of the calculated confidence intervals will contain the mean gross revenue of all soccer matches.C. We can be 99% confident that the mean gross revenue for this sample of 30 soccer matches lies in the interval.D. None of the aboveAnswers in 5 significant figures please!
Requirements: Show all working out please
