Suppose that the sitting back-to-knee length for a group of adults has a normal distribution with a mean of u = 23.4 in. and a standard deviation of o = 1.1 in. These data are often used in the design of different seats, including aircraft seats, train seats, theater seats, and classroom seats. Instead of using 0.05 for identifying significant values, use the criteria that a value x is significantly high if P(x or greater)<0.01 and a value is significantly low if P(x or less) S0.01. Find the back-to-knee lengths separating significant values from those that are not significant. Using these criteria, is a back-to-knee length of 25.7 in. significantly high? Find the back-to-knee lengths separating significant values from those that are not significant. Back-to-knee lengths greater than in. and less than in. are not significant, and values outside that range are considered significant. (Round to one decimal place as needed.)

Assume that adults have IQ scores that are normally distributed with a mean of 102.1 and a standard deviation 16.3. Find the first quartile Q1​, which is the IQ score separating the bottom​ 25% from the top​ 75%. (Hint: Draw a​ graph.)

For bone density scores that are nomally distributed with a mean of 0 and a standard deviation of 1, find the percentage of scores that are a. significantly high (or at least 2 standard deviations above the mean). b. significantly low (or at least 2 standard deviations below the mean). c. not significant (or less than 2 standard deviations away from the mean). a. The percentage of bone density scores that are significantly high is %. (Round to two decimal places as needed.) b. The percentage of bone density scores that are significantly low is %. (Round to two decimal places as needed.) c. The percentage of bone density scores that are not significant is (Round to two decimal places as needed.) %.

Suppose that the weight of seedless watermelons is normally distributed with mean 6.2 kg. and standard deviation 1.5 kg. Let X be the weight of a randomly selected seedless watermelon. Round all answers to two decimal places. A. X ~ N(  ,  ) B. What is the median seedless watermelon weight?  kg. C. What is the Z-score for a seedless watermelon weighing 8 kg?  D. What is the probability that a randomly selected watermelon will weigh more than 7 kg?  E. What is the probability that a randomly selected seedless watermelon will weigh between 4 and 5 kg?  F. The 80th percentile for the weight of seedless watermelons is  kg.