Question

A normal population has a mean of 80.0 and a standard deviation of 14.0
Question C= compute the probability of a value between 55.0 and 70.0

Answer 1

$mu=80.0$ $sigma=14.0$ calculate z-score for lower bound $x=55.0$ $%28x-mu%29%2Fsigma=%2855.0-80.0%29%2F14.0=+-1.785714286$ That rounds to -1.79 calculate z-score for upper bound $x=70.0$ $%28x-mu%29%2Fsigma=%2870.0-80.0%29%2F14.0=+-0.7142857143$ That rounds to -0.71 Now whichever way you go from here depends on what kind of table you have, or whether you use a calculator. Different books have different kinds of normal tables. If your normal table has negative values of z listed: 1. Find -0.7 in the z column. 2. Go across until you are under the .01 column 3. Read 0.2389 as the area left of -0.7 4. Find -1.7 in the z column. 5. Go across until you are under the .09 column 6. Read 0.0367 as the area left of -1.79 7. Subtract 0.2389-0.0367 8. Get 0.2022 If your normal table does not have negative values of z listed: 1. Find 0.7 in the z column. 2. Go across until you are under the .01 column 3. Read 0.2611 as the area between 0.5 and 0.71 4. Find 1.7 in the z column. 5. Go across until you are under the .09 column 6. Read 0.4633 as the area between 0.5 and 1.79 7. Subtract 0.4633-0.2611 8. Get 0.2022 Either way the probability is 0.2022. However, this is only accurate to two decimal places, since 0.71 was only accurate to two decimal places, so we should round off to 0.20. If you have a TI-84 calculator: Clear the calculator and get on the main screen Press 2nd Press VARS Press 2 You should see normalcdf( after that parentheses type this 55.0,70.0,80.0,14.0) You should see normalcdf(55.0,70.0,80.0,14.0) Press ENTER Read 0.2004524729 The calculator is much more accurate than the table. Edwin

Answer 2

A normal population has a mean of 80.0 and a standard deviation of 14.0 Question C= compute the probability of a value between 55.0 and 70.0 <pre><font size = 4 color = "indigo"><b> {{{mu=80.0}}} {{{sigma=14.0}}} calculate z-score for lower bound {{{x=55.0}}} {{{(x-mu)/sigma=(55.0-80.0)/14.0= -1.785714286}}} That rounds to -1.79 calculate z-score for upper bound {{{x=70.0}}} {{{(x-mu)/sigma=(70.0-80.0)/14.0= -0.7142857143}}} That rounds to -0.71 Now whichever way you go from here depends on what kind of table you have, or whether you use a calculator. Different books have different kinds of normal tables. If your normal table has negative values of z listed: 1. Find -0.7 in the z column. 2. Go across until you are under the .01 column 3. Read 0.2389 as the area left of -0.7 4. Find -1.7 in the z column. 5. Go across until you are under the .09 column 6. Read 0.0367 as the area left of -1.79 7. Subtract 0.2389-0.0367 8. Get 0.2022 If your normal table does not have negative values of z listed: 1. Find 0.7 in the z column. 2. Go across until you are under the .01 column 3. Read 0.2611 as the area between 0.5 and 0.71 4. Find 1.7 in the z column. 5. Go across until you are under the .09 column 6. Read 0.4633 as the area between 0.5 and 1.79 7. Subtract 0.4633-0.2611 8. Get 0.2022 Either way the probability is 0.2022. However, this is only accurate to two decimal places, since 0.71 was only accurate to two decimal places, so we should round off to 0.20. If you have a TI-84 calculator: Clear the calculator and get on the main screen Press 2nd Press VARS Press 2 You should see normalcdf( after that parentheses type this 55.0,70.0,80.0,14.0) You should see normalcdf(55.0,70.0,80.0,14.0) Press ENTER Read 0.2004524729 The calculator is much more accurate than the table. Edwin</pre>