Algebra 2 February 19, 2009. 1. A set of values has a mean of 300 and a standard deviation of 60. What value has a z-score of -1.2? 2. In a survey of.

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Presentation transcript:

Algebra 2 February 19, 2009

1. A set of values has a mean of 300 and a standard deviation of 60. What value has a z-score of -1.2? 2. In a survey of 683 car owners selected at random, 235 reported paying cash for their first car. ◦ A) Find the sample proportion ◦ B) Find the margin of error ◦ C) Find an interval likely to contain the true population proportion

 Features of a binomial experiment: 1. Repeated trials 2. Only two possible outcomes per trial 3. Probability of success is the same in each trial

 Example 1: Suppose that you guess the answers to three questions of a multiple choice test. Each question has five choices, with one correct choice. 1. What is a trial for this experiment? How many trials are there? 1. What is a success? What is the probability of success on each trial?

 Example 2: Suppose you and a friend flip a coin five times to find out who gets to play an arcade game first. The person who gets three out of five flips wins. Your winning side is heads. 1. What is a trial for this experiment? How many trials are there? 2. What is a success? What is the probability for success on each trial?

 Binomial Probability Formula: n = number of trials r = number of successes p = probability of success q = probability of failure

 Example 3: Alicia walks to school with her friend MacKenzie. MacKenzie is on time 80% of the time. What is the probability that MacKenzie will be on time 5 days in a row?

 Example 4: A fast food restaurant is attaching prize cards to every one of its soft drink cups. The restaurant awards free drinks as prizes on three out of four cards. Suppose you have three cards. Find the probability that exactly one of these cards will reveal a free soft drink as its prize.

 To find the full probability distribution for a binomial experiment, expand the binomial  Example 5: Suppose you guess on four questions on a multiple choice test. Each question has 5 choices. The probability of guessing correctly is 0.2

 Example 6: A scientist hopes to launch a weather balloon on one of the next three mornings. For each morning, there is a 40% chance of suitable weather. What is the probability that there will be at least one morning with suitable weather?

Normal Distributions

 Every normal curve has a symmetric bell shape (“the bell curve”).  The jaw widths of a population of great white sharks are normally distributed about a mean of 15.7 inches. The standard deviation is 2.8 inches. Sketch a normal curve showing the jaw widths at one, two, and three standard deviations from the mean.

TOOK OUT OF LESSON!!!  In a survey, the responses to the question “How much time do you spend at meals in one week?” were normally distributed. The mean was 13 hours. The standard deviation was 3 hours. ◦ A) What values are one standard deviation from the mean?

TOOK OUT OF LESSON!!!  In a survey, the responses to the questions “How much time do you spend in the shower daily?” were normally distributed. The mean was 15 minutes; the standard deviation was 2 minutes. ◦ A) What values are one standard deviation from the mean?

 In a Psychology class at CSU with 174 students, the final exam scores have a mean of 68.5 and a standard deviation of 7.3. The grade pattern of the exams follows a normal curve. ◦ About how many students receive grades from one to two standard deviations above the mean? ◦ About how many students receive grades of 61 or below?

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