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Score Name:_______________________________ AFM ____ / 20 The US National Sleep Foundation suggests seven to nine hours of sleep a night for adults. The Foundation conducted a survey in 2002 that suggest as many as 75% of Americans had problem sleeping, with one-third being so sleepy that it affected their daily lives. While sleep undergoes a wide variety of modifications during the human life span, all aspects have a relatively normal distribution pattern. You will be performing your own statistical study on sleep, analyzing the distribution of a sample set of data. 1. Using your TI-84+ calculator, collecting a set of data using the random number generator function. - Press MATH, move over to PRB, select #5 randInt( - Type in randInt( 1 , 14 , 50 ) STO→ L1 OR randInt( 1 , 12 , 50 ) STO 2nd 1 - This will randomly select 50 numbers between 1 and 14, inclusively and place them in List 1 - Record these numbers below from LIST 1, as numbers of hours slept each day. - These numbers, which represent a survey of 50 people’s sleep hours, will be your sample data set. Sleep hours: 2. Complete the frequency chart below based on your sample data Hours Slept 1 2 3 4 5 6 7 8 9 10 11 12 Frequ ency 3. Identify the following measurements based on your sample data. - Enter your sample data into a list on your calculator - You may use a single list OR double list - Answer to the nearest tenth Mean: _____ Q1: _____ Range: _____ Median: _____ Q3: _____ Mode: _____ Interquartile Range: _____ Standard Deviation: _____ Variance: _____ Total According to the"empirical rule", if you add percentages, you will see that approximately: • 68.1% of the distribution lies within one standard deviation of the mean. • 95.4% of the distribution lies within two standard deviations of the mean. • 99.8% of the distribution lies within three standard deviations of the mean. 4. Using the normal distribution bell curve below and your data results, identify the x _____ following: x _____ x _____ x 2 _____ x 3 _____ x 2 _____ x 3 _____ 5. Using the 50 numbers from your sample data, answer the following: a. How many of your data numbers lie within the range of ONE standard deviation? _______ b. What percent your data numbers lie within the range of ONE standard deviation? _______% Hint: Divide answer #5a by 50 c. How many of your data numbers lie within the range of TWO standard deviations? _______ d. What percent your data numbers lie within the range of TWO standard deviations? _______% Hint: Divide answer #5c by 50 e. How many of your data numbers lie within the range of THREE standard deviations? _______ f. What percent your data numbers lie within the range of THREE standard deviations? _______% Hint: Divide answer #5e by 50 6. Given the empirical rule stated above, does your data approximately follow a normal distribution pattern? Why or why not? ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________