Warm Up Mr. Clarke analyzed his Algebra 1 quiz scores to find the probability of students to achieve the following scores (max points is 12). Score 5 6.

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Presentation transcript:

Warm Up Mr. Clarke analyzed his Algebra 1 quiz scores to find the probability of students to achieve the following scores (max points is 12). Score 5 6 7 8 9 10 11 12 Prob .02 .04 .08 .14 .21 .26 .16 .09 1) Find the mean and variance for the quiz scores. 2) What is the probability a randomly selected student passed (quiz score is > 60%)?

Practice Mr. Clarke believes all his Algebra 1 students are geniuses so the quiz must have been too hard. He decides to curve the quiz by adding 2 points to each student’s score. The original scores are shown below. Score 5 6 7 8 9 10 11 12 Prob .02 .04 .08 .14 .21 .26 .16 .09 Find the mean and variance for the curved quiz scores.

Example of Combining Random Variables During the morning rush the mean number of cars entering Highway 85 from Blossom Hill Road is found to be 800 per hour with a standard deviation of 100 cars per hour. Similarly, the mean number of cars entering Highway 85 from Almaden Expressway is 1000 per hour with a standard deviation of 150 cars per hour. 1) Find the mean and standard deviation for the number of cars entering Highway 85 from these 2 roads combined.

Practice – Combining Random Variables To assemble a piece of furniture, a wood peg must be inserted into a predrilled hole. The diameter of the pegs has a mean of 2.5 inches and a standard deviation of 0.09 inches. The diameter of the holes has a mean of 2.6 inches and a standard deviation of 0.07 inches. Let X be the peg diameter and Y the hole diameter. 1) Why would the manufacturer be interested in (Y – X) ? 2) Find the mean and standard deviation of (Y – X) 3) Does it seem likely a randomly selected peg will be too big for a randomly selected hole?

Activity – Combining Random Variables On the board write the number of pets your family owns. 1) Create the probability distribution for X. 2) Find the mean and standard deviation of the random variable X. X: number of pets owned by AP Stats students in this class.

Activity – Combining Random Variables Magically, every one of your pets has been cloned! (so if you had 1 dog now you have 2 dogs). 1) Create the probability distribution for Y. 2) Find the mean and standard deviation of the random variable Y. Y: number of pets plus clones owned by AP Stats students. Compare the mean and standard deviation of Y to X. How are they related?

Activity – Combining Random Variables The cloning didn’t work out. Now, each of you is going to be randomly assigned a new sibling from the class. Both you and your new sibling are going to bring all of your pets to the new family. After finding your new sibling, write on the board the number of pets your new family has. 1) Create the probability distribution for Z. 2) Find the mean and standard deviation of the random variable Z. Z: number of pets owned by AP Stats students with their new siblings. Compare the mean and standard deviation of Z to Y and X. Are they the same or different? Why?