Statistics - The z-score of a particular x-value in a distribution is the number of standard deviations (either negative to the left or positive to the right) the x-value is from the mean. The formula is z = (x - mean)/st.dev. = (z-mu)/sigma 1 Ryan received 89 in his History exam where the mean was 70 and the standard deviation 10. In his Biology exam he received 75 when the mean was 50 and the standard deviation 12. He felt he had performed better in History than in Biology. Is this the case? Explain. (calculate the z-scores) (3 Points) 2 In international swimming the mean time for the men's 100 m freestyle is 50.46 sec with a standard deviation of 0.6 sec. For the 200 m freestyle, the mean time is 110.4 sec with a standard deviation of 1.4 sec. Jason's best time for the 100 m is 48.76 sec and for the 200 m is 108.43 sec. If he can only enter one of these events in the competition, which one should he enter? And why? (3 Points) 3 Use the Empirical Rule to the right to answer the next questions. Given an approximately normal distribution with a mean of 159 and a standard deviation of 70. What percent of values are within the interval (89, 299)? (3 Points) 4 What percent of values are within the interval (19, 159)? (3 Points) 5 What interval contains 99.7% of all values (3 Points) 6 What percent of values are above 229? (3 Points) 7 What percent of values are outside the interval (19, 229)? (3 Points) 8 The heights of RCC male students is normally distributed with a mean of 170 cm and a standard deviation of 8 cm. There are 767 male students at RCC. To the nearest whole student, how many of these males are over 180 cm? (3 Points) 9 How tall are the tallest 1% of male students? Round your answer to the nearest tenth of a cm. (3 Points) 10 Juan is in the 57th percentile of male RCC heights. How tall is Juan, to the nearest cm.? 11-A mystery number was squared (multiplied by itself) That result was then divided by ten That result then had one added to it Then that result was multiplied by 2 Then three was added Then the result was doubled Then one was added. Then the number was divided by 3. The result of all of this was the number 7 =Themysterynumber= Enter your math answer 12- It takes 1 hour 20 minutes to drive to the airport, yet the return trip takes only 80 minutes using the same route and driving at the same speed. How can this be