Construct a probability distribution and calculate its summary statistics. Then/Now

Copy in your notes pg664 Key Concept 1

With your partner, answer the following questions (2 minutes): Classify Random Variables as Discrete or Continuous With your partner, answer the following questions (2 minutes): A. Classify the random variable X as discrete or continuous when X represents the number of times a phone rings before being answered. Explain your reasoning. B. Classify the random variable X as discrete or continuous when X represents the amount of time between when a phone first rings and when it is answered. Explain your reasoning. Example 1

With your partner, answer the following questions: Classify Random Variables as Discrete or Continuous With your partner, answer the following questions: A. Classify the random variable X as discrete or continuous when X represents the number of times a phone rings before being answered. Explain your reasoning. Discrete; the number of rings is countable. B. Classify the random variable X as discrete or continuous when X represents the amount of time between when a phone first rings and when it is answered. Explain your reasoning. Continuous; the time could be any time in a reasonable interval. Example 1

Copy in your notes-page 665 Key Concept 2

Copy example 2A with work shown: Construct a Probability Distribution Copy example 2A with work shown: 2A. MOVIE RATINGS Movie-goers were asked to rate a movie. The possible ratings were 1 for poor, 2 for average, and 3 for good. Use the frequency distribution shown to construct and graph a probability distribution for the random variable X. Example 2

Construct a Probability Distribution To find the probability that X takes on each value, divide the frequency of each value by the total number of movie ratings, which is 12 + 14 + 37 or 63. P(1) = or 0.19 P(2) = or 0.22 P(3) = or 0.59 Example 2

Construct a Probability Distribution The probability distribution of X is shown in the table and graph below. Answer: CHECK All of the probabilities in the table are between 0 and 1 and .  Example 2

Solve with partner (5 minutes) 2B. ONLINE SHOPPING A rating survey was conducted about the ease of using an online shopping site. The results are shown in the table. Use the frequency distribution to construct and graph a probability distribution. Example 2

2B. ONLINE SHOPPING A rating survey was conducted about the ease of using an online shopping site. The results are shown in the table. Use the frequency distribution to construct and graph a probability distribution. Example 2

Copy in notes-page 666 Key Concept 3

Copy example 3A with work shown: Mean of a Probability Distribution Copy example 3A with work shown: 3A. MOVIE RATINGS The table shows the probability distribution from Example 2. Find the mean score and interpret its meaning in the context of the problem situation. Example 3

Therefore, the mean μ of this probability distribution is about 2.4. Mean of a Probability Distribution Multiply each score by its probability and find the sum of these products. Organize your calculations by extending the table. Therefore, the mean μ of this probability distribution is about 2.4. Answer: 2.4; The movie is considered between average and good by movie-goers. Example 3

Solve with partner (3 minutes) 3B. ONLINE SHOPPING The table shows the probability distribution from Example 2, Guided Practice. Find the mean score and interpret its meaning in the context of the problem situation. Example 3

Solve with partner (3 minutes) 3B. ONLINE SHOPPING The table shows the probability distribution from Example 2, Guided Practice. Find the mean score and interpret its meaning in the context of the problem situation. 2.27; The online site is considered good by its users. Example 3

Homework: p.671 #1-9 (for questions 7,8,9 don’t find variance and standard deviation), 35, 49, 51,56,57