(1) The ages and heights of a sample of child smokers were taken. The average age was 13.5 years, with an SD of 2.3 years. The average height was 167.5 cm, with an SD of 8.2 cm. Moreover, the correlation between age and height was 0.18. Find the regression equation for predicting height from age.
(2) Three cards are dealt off the top of a well-shuffled deck. Find the following: (a) The chance that all three of them are diamonds.
(b) The chance that the second card is a diamond.
(3) Life expectancies for men and women were measured by country. It was found that the average male life expectancy was 71.8 years with an SD of 7 years, and that the average female life expectancy was 77.4 with an SD of 7.3 years. Moreover, the correlation between male and female life expectancies was found to be 0.95. Use this information to estimate female life expectancy in a country where the male life expectancy is 62.8 years.
(4) Determine whether the following statement is true or false, and justify your answer: If E and F are mutually exclusive events, then the sum of the chance of E occurring and the chance of F occurring must add up to 100%.
(5) Determine whether the following statement is true or false, and justify your answer: If the RMS error for predicting Y from X is equal to 1, then the correlation between Y and X is equal to 0.
(6) If a fair six-sided die is rolled three times, find the probability that at least one of the three rolls is less than 6.