MATH 1342 Written Homework: Distributions. CH 4 - 6 Name: Section: . Show All Work For Full Credit! Provide an appropriate response. Use the calculator or Standard Normal Table to find the probability if needed. Problem 1: State whether the variable is discrete or continuous: -

The height of a player on a basketball team - The number of goals scored in a soccer game - The speed of a car on a Los Angeles freeway during rush hour traffic - The age of the oldest student in a statistics class - The number of pills in a container of vitamins Problem 2: Four hundred tickets are sold at $10 each. Two tickets will be randomly selected, and the winners will receive a prize of $200 each. What is the expected value for a person that buys one ticket? Problem 3: At a raffle, 10,000 tickets are sold at 10 each for three prizes valued at $2,500, $1,200, and $400. What is the expected value of one ticket? Problem 4: All distributions have their specific characteristics. a. What are the characteristics of the discrete probability distribution function? b. What are three characteristics of a binomial experiment? c. What can you tell about outcomes of continious probability distribution? What are the graph and the area under the graph for this distribution? What is P(x = a)? Problem 5: The average age a child says the very first word can be as early as 6 months, or as late as 18 months. a. Write the function and graph the distribution, if the age, when the child says the first word, is uniformly distributed. b. Find the mean and the standard deviation. c. What is the probability that the child says the first word between 10 and 12 month? d. What is the 80th percentile of the distribution? e. Find the probability that a child says the first word before she/he turns 15 month, if the child is already one year old? Problem 6: In a recent survey, 80% of the community favored building a police substation in their neighborhood. If 15 citizens are chosen, what is the mean number and the standard deviation of the number favoring the substation? Problem 7: The probability that an individual is left-handed is 0.16. In a class of 10 students, what is the mean and standard deviation of the number of left-handers in the class? Problem 8: The probability that a house in an urban area will be burglarized is 5%. If 20 houses are randomly selected, how many houses would you expect to be burglarized? Problem 9: Seventy percent of adults ages 50 and older want to reach their 100th birthday. You randomly select five adults ages 50 and older and ask them whether they want to reach their 100th birthday. The random variable represents the number of adults ages 50 and older who want to reach their 100th birthday. Graph the binomial distribution using a histogram and describe its shape (i.e. find the P(X = x) for each of the X) Problem 10: Find the z-score that corresponds to the given area under the standard normal curve. a. b. c. d. Find the z-scores for which 90% of the distribution's area lies between -z and z. e. Find the z-scores for which 98% of the distribution's area lies between -z and z. f. Find the z-score for which 99% of the distribution's area lies between -z and z. Problem 11: Find the area under the standard normal curve to the left of z = 1.5. Problem 12: Find the area under the standard normal curve to the right of z = 1. Problem 13: Find the area under the standard normal curve between z = 1 and z = 2. Problem 14: Find the area under the standard normal curve between z = 1.5 and z = 2.5. Problem 15: Find the sum of the areas under the standard normal curve to the left of z =-1.25 and to the right of z = 1.25.