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Honors Statistics S6-2 Applications of the Normal Distribution NAME________________________ BLOCK_______________________ Questions 1 – 7, draw the normal distribution and label all appropriate areas on your diagram. 1. What is the probability that a normally distributed random variable is not within 1.5 standard deviations of the mean? 2. Many students planning to go to college take the SAT examination. This test is nationally normed with a mean of 540 and a standard deviation of 90. If Joe received a 625 mathematics score, what was his percentile score? 3. The mean and standard deviation of a normal distribution is 53 and 6 respectively. Find the percentage of scores that are greater than 60. 4. A random variable x is normally distributed with a mean of 420 and a standard deviation of 35. How many standard deviations is a score of 381 from the mean? 5. The sizes of the fish in a lake are normally distributed with a mean of 4.8 lbs. and a standard deviation of 1.3 lbs. Through a catch and release program, park rangers estimate that there are approximated 850 fish is the lake. Approximately how many fish weigh between 5 and 5.4 lbs.? 6. A random variable x is normally distributed with an unknown mean and a standard deviation of 7.24. If a score greater than 62 occurs approximately 85% of the time, find the mean of this distribution to the nearest hundredth. 7a. Draw a normal curve that has a mean of 182 and a standard deviation of 18. Label 3 standard deviations from the mean. b. Using the distribution drawn in part a above, what is the probability that a score lies between 174 and 186. Give your answer to 4 decimal places. 7b________ c. Using the distribution drawn in part a above, what is the probability that a score lies between 166 and 176. Give your answer to 4 decimal places. 7c________ d. What is the minimum score to be in the top 8%. 7d________