A computer selects a number X from 1 to 9 randomly and uniformly. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ U( , ) b. Suppose that the computer randomly picks 35 such numbers. What is the distribution of 3': for this selection of numbers. E - N( , ) c. What is the probability that the average of 35 numbers will be less than 4.2? Treat the number of months X after January 1 that someone is born as uniformly distributed from 0 to 12. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ U( , ) b. Suppose that 38 people are surveyed. What is the distribution of :Y: for this sample? 5: N( , ) c. What is the probability that the average birth month of the 38 people will be less than 7.3? Suppose that the age of students at George Washington Elementary school is uniformly distributed between 5 and 11 years old. 49 randomly selected children from the school are asked their age. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X U( , ) Suppose that 49 children from the school are surveyed. Then the sampling distribution is b. What is the distribution of 5:? 5?; ~ N( , ) c. What is the probability that the average of 49 children will be between 8 and 8.2 years old? The number of seconds X after the minute that class ends is uniformly distributed between 0 and 60. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ U( , ) then the sampling distribution is b. Suppose that 35 classes are clocked. What is the distribution of :E for this group of classes? :7: - N( , ) c. What is the probability that the average of 35 classes will end with the second hand between 23 and 26 seconds? A random number generator picks a number from 4 to 48 in a uniform manner. Round answers to 4 decimal places when possible. a. The mean of this distribution is b. The standard deviation is c. The probability that the number will be exactly 16 is P(x = 16) = cl. The probability that the number will be between 7 and 34 is P(7 35) = f. P(x>19 | x 2.74) = f. P(x>2.9 | x> 0.1) = g. Find the 30th percentile. h. Find the maximum for the lower quartile. The time that it takes for the next train to come follows a Uniform distribution with f(x) =1/20 where x goes between 6 and 26 minutes. Round answers to 4 decimal places when possible. a. This is a distribution. b. It is a distribution. c. The mean of this distribution is d. The standard deviation is e. Find the probability that the time will be at most 23 minutes. f. Find the probability that the time will be between 13 and 17 minutes. g. Find the 515t percentile. h. Find the probability that the time is more than 20 minutes given (or knowing that) it is at least 14 minutes. A bus comes by every 14 minutes. The times from when a person arives at the busstop until the bus arrives follows a Uniform distribution from 0 to 14 minutes. A person arrives at the bus stop at a randomly selected time. Round to 4 decimal places where possible. a. The mean of this distribution is b. The standard deviation is c. The probability that the person will wait more than 7 minutes is d. Suppose that the person has already been waiting for 1.5 minutes. Find the probability that the person's total waiting time will be between 2.7 and 5 minutes e. 23% of all customers wait at least how long for the train? minutes. The age of children in kindergarten on the first day of school is uniformly distributed between 4.8 and 5.75 years old. A first time kindergarten child is selected at random. Round answers to 4 decimal places if possible. a. The mean of this distribution is b. The standard deviation is c. What is the probability that the child will be older than 5.1 years old? d. The probability that the child will be between 5.2 and 5.4 years old is e. If such a child is at the 27th percentile, how old is that child? years old. The time it takes me to wash the dishes is uniformly distributed between 5 minutes and 12 minutes. What is the probability that washing dishes tonight will take me between 7 and 9 minutes? Give your answer accurate to two decimal places. The time it takes me to wash the dishes on a randomly selected night is uniformly distributed between 5 minutes and 16 minutes. a) State the random variable in the context of this problem. 0 rv X = washing dishes 0 rv X = a randomly selected night 0 rv X = a uniform distribution 0 rv X = the time it takes me to wash dishes on a randomly selected night b) Compute the height of the uniform distribution. Leave your answer as a fraction. c) Which of the following is the correct description of the picture of the probability distribution of X? O a bell-shaped curve that starts at 5 and ends at 16 O a rectangle with edges at 5 and 16 d) What is the probability that washing dishes tonight will take me between 8 and 15 minutes? Give your answer as a fraction. Give your answer accurate to three decimal places. e) What is the probability that washing dishes tonight will take exactly 8 minutes