Bluman A.G. Elementary Statistics- A Step By Step Approach

Section 6–1 Normal Distributions 31348. Find two z values so that 48% of the middle area isbounded by them. z 0.6449. Find two z values, one positive and one negative, thatare equidistant from the mean so that the areas in thetwo tails total the following values.a. 5% z 1.96 and z 1.96 (TI: 1.95996)b. 10% z 1.65 and z 1.65, approximately(TI: 1.64485)c. 1% z 2.58 and z 2.58, approximately (TI: 2.57583)Extending the Concepts50. In the standard normal distribution, find the values of z forthe 75th, 80th, and 92nd percentiles. 0.6745; 0.8416; 1.4151. Find P(1 z 1), P(2 z 2), and P(3 z 3).How do these values compare with the empirical rule?0.6827; 0.9545; 0.9973; they are very close.52. Find z 0 such that P(z z 0 ) 0.1234. 1.1653. Find z 0 such that P(1.2 z z 0 ) 0.8671. 2.1054. Find z 0 such that P(z 0 z 2.5) 0.7672. 0.7555. Find z 0 such that the area between z 0 and z 0.5 is0.2345 (two answers). 1.45 and 0.1156. Find z 0 such that P(z 0 z z 0 ) 0.76. 1.17557. Find the equation for the standard normal distributionby substituting 0 for m and 1 for s in the equationy eXm2 2s2 s2pe X 2 2y 2p58. Graph by hand the standard normal distribution byusing the formula derived in Exercise 57. Let p 3.14and e 2.718. Use X values of 2, 1.5, 1, 0.5, 0,0.5, 1, 1.5, and 2. (Use a calculator to compute the yvalues.)Technology Step by StepMINITABStep by StepThe Standard Normal DistributionIt is possible to determine the height of the density curve given a value of z, the cumulativearea given a value of z, or a z value given a cumulative area. Examples are from Table E inAppendix C.Find the Area to the Left of z 1.391. Select Calc>Probability Distributions>Normal. There are three options.2. Click the button for Cumulative probability. In the center section, the mean and standarddeviation for the standard normal distribution are the defaults. The mean should be 0, andthe standard deviation should be 1.3. Click the button for Input Constant, then click inside the text box and type in 1.39. Leavethe storage box empty.4. Click [OK].6–15