The average score for games played in the NFL is 21.3 and the standard deviation is 9.2 points. 41 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution. What is the distribution of ¯x? x¯ ~ N( , ) What is the distribution of ∑x ? ∑x ~ N( , ) P(¯x< 21.1448) =  Find the 78th percentile for the mean score for this sample size. _____ P(21.9448 < x¯ < 22.3184) =  Q3 for the x¯ distribution =  P(∑x < 817.7368) =

A standardized exam's scores are normally distributed. In a recent year, the mean test score was 21.4 and the standard deviation was 5.3. The lest scores of four students selected at random are 15, 24, 8, and 36. Find the z-scores that correspond to each value and determine whether any of the values are unusual The 2-score for 15 is (Round to two decimal places as needed) The 2-score for 24 is (Round to two decimal places as needed.) The z-score for 8 is (Round to two decimal places as needed) The 2-score for 36 is (Round to two decimal places as needed) Which values, if any, are unusual? Select the correct choice below and, if necessary, fill in the answer box within your choice. OA. The unusual value(s) is/are (Use a comma to separate answers as needed.) OB. None of the values are unusual

The average number of miles (in thousands) that a car's tire will function before needing replacement is 68 and the standard deviation is 12. Suppose that 15 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution. What is the distribution of X? X ~ N(___,___) What is the distribution of ¯x? x¯ ~ N(___,____) If a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between 65 and 66.8. ______ For the 15 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 65 and 66.8. _______ For part d), is the assumption that the distribution is normal necessary? __Yes ___ No

Systolic blood pressure readings are normally distributed with a mean of 121 and standard deviation of 15. If a person from the population was selected at random, find the probability that their blood pressure is in the acceptable range (between 114 and 140) for an athletic activity.  A. Label and shade the normal distribution curve to model this problem.