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Stat104-Section5-sol

# Stat104-Section5-sol - Stat 104 Section 5 Handout Solutions...

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Stat 104, Section 5 Handout Solutions Benny, Thursday, 4:00pm, SC 309 Key concepts Continuous Random Variables Le Normal Distribution Sample distribution of ¯ X (implicit dependence on the central limit theorem) t-distirbution Confidence intervals Practice Problems 1. The daily high temperature for the first week in October in Boston is approximately Normally distributed with an average high of 66 F and a standard deviation of 7 F. a. What is the probability that a day in the first week of October would have a high of 57.8 F or colder? Let X be a variable to represent the temperature for a day inthe first week of October. We want P ( X 57 . 8). Assuming normality, we calculate the z-score z = X - ¯ X σ X = 57 . 8 - 66 7 = - 1 . 17 Referring to the z-value probability table, we get P ( z < - 1 . 17) 12% b. What high temperature needs to be achieved in order to be in the bottom 1% of the daily high temperatures in the first week of October? We do the reverse of part a. Specifically, we find z low satisfying P ( z < z low ) = . 01 And find z low = - 2 . 33. Converting this into the temperature scale with the standard deviation, we have T low = 66 - 2 . 33 * 7 = 49 . 7 1

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Stocks We have a dataset of S&P index returns for the last 2 decades. The object of our study is the daily percentage return of the stocks. Note that these are percentage points, so a 2% return has a value
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