MAT 223, Probability Distributions, Spring 2017Name ______

Instructions: For each problem below, a) determine if the problem belongs to a binomial distribution or a normal distribution, b) if it is binomial, determine if it is exact or cumulative, c) calculate the indicated probability.

  1. The probability that a lightbulb works coming out of the package new is 98%. A store owner buys 20 light bulbs. What is the probability that all the light bulbs work? What is the probability that 18 or more work?
  1. What is the probability that you will have fewer than 6 heads in 14 coin flips if the coin is fair?
  1. A variable is normally distributed with a mean of 41.2 and a standard deviation of 12.3. A researcher wants to examine the bottom 10% of the distribution more closely. What is the value at the top of the bottom 10%?
  1. If you roll a fair tetrahedral (4-sided) die 12 times, what is the probability of getting exactly three 4s?
  1. According to a survey, 63% of murders committed last year were cleared by arrest or exceptional means. 50 murders committed last year are randomly selected, and the number of cases cleared is recorded. What is the probability that exactly 40 of the cases will be cleared? Would it be unusual if fewer than 20 cases were cleared?
  1. A test has a mean score of 81 and a standard deviation of 6.4. A student scores on 90 on the test. What is the probability of receiving this score or higher? What percentile does the score represent?
  1. The US Army requires women’s heights to be between 58 inches and 80 inches. What percentage of women meet that requirement if the mean of women’s height is 64 inches and the standard deviation is 3 inches? How many women in the US could be denied admission to the Army on account of their height is 2% of the population of 350 million has considered applying?
  1. If the ACT has a mean of 21 with a standard deviation of 5.2, what is the score that would put a student in the top 15% of the test? Round to the nearest integer.
  1. According to a survey, 21% of residents of a country 25 years or older had earned at least a bachelor’s degree. You are performing a study and would like at least 10 people in the study to have earned a bachelor’s degree. How many residents of the country in this category do you expect to randomly select if the sample size is 20? What if it’s 50?
  1. What is the probability of rolling the dice 15 times and getting exactly two 6s?
  1. A student took an exam whose mean is 78 with a standard deviation of 12. What is the probability of receiving a passing score?
  1. What is the probability of rolling a 20-sided die 50 times and obtaining 11 numbers divisible by 3? Write your solution using the binomial formula. How would you enter this into your calculator?
  1. If the probability that a randomly selected person has blue eyes is 37% in a certain population, what is the probability of selecting 20 people and 10 or more of them have blue eyes?
  1. A variable is normally distributed with a mean of 11 and a standard deviation of 2.4. What is the probability of scoring between 6 and 13?
  1. A variable is normally distributed with a mean of 1561 with a standard deviation of 103. Find the probability of being less than 1400 or greater than 1770.
  1. If the probability of having voted in the last Presidential election in the US is 63%, what is the probability that in a randomly selected sample of 10 people that fewer than half them voted in the last election?
  1. Which of the following scenarios can use a binomial variable to calculate the probability?
  1. Getting a 6 on the 10-sided die?
  2. Your favorite color is blue?
  3. How tall you are?
  4. How long it takes between customers at a drive-thru window?
  5. Randomly choosing a Republican in a survey?
  6. The number of coin flips needed to get 5 heads?
  7. Choosing three marbles from a bag of 30?