# in pounds lbs We will treat a subset of this dataset as a

Last updated: 2/2/2024

in pounds lbs We will treat a subset of this dataset as a representative sample of realized values for our random variable The first five rows of the data look like this Weight in lbs 4 9 12 0 9 2 9 5 6 1 Import the dataset into SALT for analyzing After you have clicked the tab for your selected topic and read the problem answer the questions below a Create a histogram in SALT to determine if the distribution of our sample is mound shaped and symmetric with no outliers When a data s distribution is mound shaped and at least roughly symmetric with no outliers a normal distribution can be used to model the variable s behavior USE SALT Since the histogram for our sample is mound shaped and is O at least roughly symmetric with no outliers the normal distribution can be used to approximate the behavior for this random variable b Locate the sample mean and standard deviation for our variable Round your answers to four decimal places X X S c Draw the normal distribution with a mean of x and a standard deviation of s on SALT s Distribution Calculators page Round your answers to two decimal places The random variable value that is predicted to be one standard deviation above the mean is The random variable value that is predicted to be two standard deviations below the mean is The random variable that is predicted to have a z score of 3 00 is X x x x d Use the Probability and Z Score sections on the left panel and radio buttons on the right panel to answer the following questions Remember to convert the percentage to a proportion before entering the value into SALT Round your answers to four decimal places Approximately 2 8 of values for our random variable are predicted to be larger than what value Approximately 90 of values for our random variable are expected predicted to be centered around the mean with a lower value of X and an upper value of The Z scores for these two values are Z X and z e How well is the normal distribution modeling the random variable represented by our sample data Use SALT s data filters and Descriptive Statistics page to answer the following questions In part d you found the boundary values where the normal model predicts the middle 90 of data values are located Use the filters on the Dataset page to filter out observations that are outside of this range then return to the Descriptive Statistics page to locate the number of sample values within this region There are sample values within this region Remove the filter and return to the Descriptive Statistics page There are values in the entire sample Use these two counts to determine the actual proportion of sample values within this region Rounded to three decimal places the proportion of sample values within this middle region is How different are the actual and predicted proportions Subtract the predicted proportion from the actual proportion and take the absolute value of the result to determine how different they are Calculate the following quantity difference in proportions actual proportion predicted proportion Also in part d you found the boundary value that the normal model predicts 2 8 of values are larger than Enter this value into SALT s data filter and determine the number of sample values that meet this criteria There are sample values within this region Use this count and the size of the sample to determine the actual proportion of sample values within this region Rounded to three decimal places the proportion of sample values within this region is How different are the actual and predicted proportions Subtract the predicted proportion from the actual proportion and take the absolute value of the result to determine how different they are Calculate the following quantity difference in proportions actual proportion predicted proportion