PSTAT Cheat Sheet

# PSTAT Cheat Sheet - 1. Two fair dice are rolled and the sum...

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1. Two fair dice are rolled and the sum calculated. If the sum totals a 2 or 11, win \$5. If the sum totals a 5 or 10, you win \$2. And for all other rolls, you lose \$1. Let Y = the amount of money won. a) Construct a pdf for Y b) Find the expected value of Y c) Would you play this game? Justify your answer 2. 38 students sign up for a GRE prep course. Upon enrolling, the class average was 1140. At the conclusion of the 5-week course, the average was 1190 with a standard deviation of 92. a) Construct a 95% Confidence Interval for the average GRE score after taking the prep course. Is there evidence that this prep course increases GRE scores? b) Confirm your result by conducting a Hypothesis Test using a 5% significance level 3. Timmy grabs a stack of 8 quarters to do some laundry. After accidentally dropping the quarters, he claims, “6 heads” without looking. Find the probability this actually occurs. 4. The average transaction at a certain Starbucks is \$4.85 with a standard deviation of \$1.15. In a random sample of 75 customers, find the probability that their total sales are under \$375 5. The Following data has been gatherer on used car sales: a) Obtain the regression line. Interpret the meaning of the slope and y-intercept b) Find and comment on the coefficient of determination c) Test if the regression line is statistically significant at a 5% significance level. d) Find a 90% prediction interval for the number of cars sold in a month when 14 commercials are broadcast

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6. IQ scores are normally distributed with mean 100 and standard deviation 16. What IQ score corresponds to the 45 th percentile? 7. In the parking lot of a high tech company, 35% of the cars parked are US made and of these, 20% are luxury cars; 65% are
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## PSTAT Cheat Sheet - 1. Two fair dice are rolled and the sum...

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