What percent of a standard normal distribution N(;4 = 0; 0' = 1) is found in each region? Be sure to draw a graph. (Round your answers to the nearest whole number.) (a) Z 1.42 % (c) 0.43 2.5 \"/0 A survey was conducted by a psychology student at a local university. One question asked randomly selected respondents to estimate how many minutes each day they experienced stress. IQ USE SALT (a) Is the average number of minutes that the randomly selected students experienced stress a parameter or a statistic? parameter 0 statistic V (b) The mean number of minutes that students experienced stress each day was 25.8 minutes with a standard deviation of 5.4 minutes. What is the z-score of a respondent who felt stressed for 20 minutes? (Round your answer to two decimal places.) (c) Determine whether the following statement is true or false. If the time respondents felt stressed was recorded in seconds instead of minutes, the z-score would stay the same. 0 True False I (a) If you create a histogram of the judges' ratings across all contestants, the graph appears to be approximately which of the following? (' left skewed 0 normal x\" uniform (7 right skewed q! (b) The judge rates you with a z-score of 1.30. This corresponds to which percentile (in percent)? (Use a table or technology. Round your answer to two decimal places.) % (c) The 90th percentile qualies a DECA competitor for the "Exceeds Expectations" rating. Does your zscore of 1.30 qualify you for the "Exceeds Expectations" category? To get from your dorm to your rst class of the day, you ride your bicycle across campus. Suppose that travel times follow a normal distribution with a mean time of 8 minutes with a standard deviation of 2 minutes. IA USE SA (a) One morning you wake up late, and you have only 5 minutes to make it to class. What is the z-score for the 5-minute trip? -1.5 (b) Using the Empirical Rule, what is the probability that it takes less than 2 minutes to arrive to class? 0.8414 x (c) What is the probability that it takes less than 5 minutes to arrive to class? (Use a table or technology. Round your answer to four decimal places.) 0.0668 (d) What is the probability that it takes between 5 and 10 minutes to arrive to class? (Use a table or technology. Round your answer to four decimal places.) 0.7745 q The lengths of songs played on the radio follow an approximately normal distribution. lg USE SALT (a) Calculate the z-score representing the longest 25% of lengths of songs played on the radio. (Use a table or technology. Round your answer to two decimal places.) (b) If the mean length of songs is 3.56 minutes with a standard deviation of 0.25 minutes, calculate the z-score for a song that is 4 minutes long. (c) Is the 4-minute-long song in the top 25% of songs played? 0 Yes 'i No J Consider the following two distributions for GRE scores: N04 = 150; a = 7) for the verbal part of the exam and My = 155; o' = 7.72) for the quantitative part. Use this information to compute each of the following questions. (Round your answers to the nearest integer.) (a) The score of a student who scored in the 80th percentile on the Quantitative Reasoning section. (b) The score of a student who scored worse than 70% of the test takers in the Verbal Reasoning section. A reference states that average daily high temperature in June in a particular city is 86F with a standard deviation of 7F, and it can be assumed that they to follow a normal distribution. We use the following equation to convert F (Fahrenheit) to C (Celsius): 5 c: F32 _ ( )x9 (a) Write the probability model for the distribution of temperature in C in June in this city. (Round your standard deviation to four decimal places.) ~(u= \"7,6: ) (b) What is the probability of observing a 34C (which roughly corresponds to 93.2F) temperature or higher on a randomly selected day in June in this city? Calculate using the C model from part (a). (Round your answer to four decimal places.) (c) The probability of observing a 93.2F temperature or higher on a randomly selected day in June in this city is approximately 0.1518. Did you get the same answer or a different answer in part (b)? Are you surprised? Explain. ' The two sets of calculations produced very different answers which isn't surprising since the conversion formula had to be applied to the numbers. ' The two sets of calculations produced very different answers which isn't surprising since once we standardize the Z-scores are the different. " The two sets of calculations produced very different answers which isn't surprising since the means and the standard deviations of the two distributions are different. " Both sets of calculations produced approximately the same answer which isn't surprising since the means and the standard deviations are the same. 0 Both sets of calculations produced approximately the same answer which isn't surprising since once we standardize the Z-scores are the same. (d) Estimate the IQR of the temperatures (in C) in June in this city. (Round your answer to two decimal places.) El Part (B) For 2012, the SAT math test had a mean of 514 and standard deviation 117. The ACT math test is an alternate to the SAT and is approximately normally distributed with mean 21 and standard deviation 5.3. If one person took the SAT math test and scored 700 and a second person took the ACT math test and scored 31, who did better with respect to the test they took? (Round your answers to two decimal places.) The z-score for an SAT score of 700 is 1.59 . The z-score for an ACT score of 31 is 1.71 X . Therefore, the student who took the ACT v did better, because that person has a higher , , z-score