hw7

IE3302 HW#7 (Ch 8) Due by end of day Fri 4/9 To be worked individually. Calculated values may be given in fraction or decimal form; if in decimal form must be rounded to 4 decimal places . 100pt assignment. To be worked individually. All problems to be submitted in order, in a single Word or PDF document, to the Hw#7 Moodle dropbox. If handwritten & scanned, or use handwritten with digital ink, ensure that all solutions are legible before submitting. Work must be shown for credit. All problems 10pts each. 1. A food delivery service has delivery times with known  =45 minutes and  =12 minutes. A sample of 36 delivery times is taken. a. What is the probability the sample mean will be > 48 minutes? 0.0668 b. What is the probability the sample mean is between 44 and 49 minutes? 0.6331 c. If 100 samples were collected, and the sample mean was 65 minutes, what would you conclude? There are many outliers in the 100 samples collected. 2. Given X~b(x;10,0.2). a. For a sample size of 50, what is the probability of the sample mean being between 1.9 and 2.3? 0.9996 b. Give the Excel formula to find the probability of ´ X being less than 1.9. =NORM.DIST(1.9, 2, 0.09798, TRUE) c. What is the minimum sample size needing such that the standard error is no more than 0.01? 400 3. Given observations X i ~ NORM( 40, 0.25 ) inches. A sample of 36 observations is taken from the population with ´ X = 40.01. a. Pr( ´ X > 40.02)? 0.0228 b. What is the probability of ´ X being at least as far from the mean as the sample above ( ´ X = 40.01)? 0.0456 c. Calculate +/- 3 sigma control limits for ´ X . Would the sample taken above fall within or outside the limits? What conclusion do you draw from this? The control limits are 39.35 and 40.75, the same take above would fall into these limits which suggest that the sample is consistent with the expected variability. 4. 50 observations are collected from an EXPONENTIAL distribution with a mean of 20 hours. ´ X =20.4 hours and S=22.3 hours (note: since you know the Xi~EXPO(), you also know  ). a. What is the probability of getting a sample mean at least this far from the population mean? 0.17 b. What is the probability of getting an S this far or further above the population standard deviation? 0.0606 5. The average height of students at a university has historically been 174.5cm and is believed to be approximately normally distributed. The  is not known, but from a random sample of 10 students, S=7.5cm.