ind the mean and standard deviation for each uniform continuous model. (Round "Mean" answers to 1 decimal place and "Standard deviation" answers to 4 decimal places.) Standard Deviation U0, 14) U(120, 240) U2, 93) Joan's finishing time for the Bolder Boulder 10K race was 1.71 standard deviations faster than the women's average for her age group. There were 375 women who ran in her age group. Assuming a normal distribution, how many women ran faster than Joan? (Round down your answer to the nearest whole number.) Nmborcfwomen T High school students acrass the nation compete in a financial capability challenge each year by taking a National Financial Capability Challenge Exam. Students who score in the top 13 percent are recognized publicly for their achievement by the Department of the Treasury. Assuming a normal distribution, how many standard deviations above the mean does a student have to score to be publicly recognized? (Round your answer to 2 decimal places.) Standard deviations | | Last year's freshman class at Big State University totaled 5,340 students. Of those, 1,252 received a merit scholarship to help offset tuition costs their freshman year (although the amount varied per student). The amount a student received was M$3,462, $482). If the cost of full tuition was $4,150 last year, what percentage of students who received a merit scholarship did not receive enough to cover full tuition? (Round your answer to the nearest whole percent.) porcentage ofstugents [ [ | Suppose X /59, 7). Write the Excel function to find the X values associated with the following percentages: a. Highest 18 percent O =NORMS.INV(0.82,59,7) O =NORM.INV(82,59,7) O =NORM.INV(0.82,59,7) b. Middle 60 percent O Xupper =NORMS.INV(0.82,59,7), Xlower =NORMS.INV(0.2,59,7) O Xupper =NORM.INV(0.2,59,7), Xlower =NORM.INV(0.82,59,7) O Xupper =NORM.INV(0.8,59,7), Xlower =NORM.INV(0.2,59,7) c. Lowest 22 percent O =NORM.INV(0.78,59,7) O =NORM.INV(0.22,59,7) O =NORMS.INV(0.22,59,7)The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 380 grams and a standard deviation of 16 grams. Find the weight that corresponds to each event. (Use Excel or Appendix C to calculate the z-value. Round your final answers to 2 decimal places.) Highest 20 percent _ Middle 60 percent _m_ Highest 80 percent Lowest 15 percent _ e Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 24% below the target pressure. Suppose the target tire pressure of a certain car is 30 psi (pounds per square inch.) (a) At what psi will the TPMS trigger a warning for this car? (Round your answer to 2 decimal place.) whentesropeeres [ [ Jem | (b) Suppose tire pressure is a normally distributed random variable with a standard deviation equal to 2 psi. If the car's average tire pressure is on target, what is the probability that the TPMS will trigger a warning? (Round your answer to 4 decimal places.)