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AP STATISTICS Quiz-6.1 Discrete and Continuous Random Variables Last 4 of Student ID____________ Period______ 1. Imagine selecting a U.S. high school student at random. Define the random variable X=number of languages spoken by the randomly selected student. The table below gives the probability distribution of X, based on a sample of students from the U.S. Census at School database: Languages: 1 2 3 4 5 Probability: 0.630 0.295 0.065 0.008 0.002 (a) Is this a legitimate probability distribution? Explain how you know. Yes, since the probabilities add to 1. (b) Make a histogram of the probability distribution. Describe what you see. Center: Median=1 Unusual Features: There are outliers above 3.5 (4&5) Shape: Skewed Right Spread: Range-5 – 1 = 4 and IQR-2 – 1 = 1 (c) What is the probability that a randomly selected student speaks at least three languages? P(X≥3)=0.065+0.008+0.002=0.075 (d) Compute the mean of the random variable X and interpret this value in context. µX=the mean number of languages spoken by U. S. high school students in the long run=1.457 (e) Compute and interpret the standard deviation of the random variable X. 𝝈X=the typical distance from the mean (1.457) for each U. S. high school student=0.6709 2. The weight of 3-year-old females closely follow a Normal distribution with a mean of µ=30.7 pounds and a standard deviation of 3.6 pounds. (a) What is the probability that a randomly selected 3-year-old female weighs at least 30 pounds? P(X≥30) normalcdf(30,100,30.7,3.6)=0.577 (b) What is the probability that a randomly selected 3-year-old female weighs less than 30 pounds? P(X<30) normalcdf(0,30,30.7,3.6)=0.423 (c) What is the probability that a randomly selected 3-year-old female weighs between 25 and 35 pounds? P(25<X<35) normalcdf(25,35,30.7,3.6)=0.827