2 . For a sample of 289 female heights , the mean was 65.3 inches and the standard deviation was 2.8 inches . The shortest person in this sample had of 56 inches . a . Find the z-score for the height of 56 inches . b . What does the negative sign for the z-score represent ? c . Is this observation a potential outlier according to the three standard deviation distance criterion ? Explain . 3 . A company decides to investigate the amount of sick leave taken by its employees . A sample of seven employees yields the following numbers of days of sick leave taken in the past year . 1 1 3 0 1 6 2 Use this information to answer parts a through c . 4 . What is the effect of the outlier ? 5 . A survey asked 6189 random adults the question “ How many children have you ever had ?” Use the results shown below to answer the following questions . # no of children 0 1 2 3 4 5 6 7 n 1851 869 1462 945 494 281 153 93 a . Find the standard error of the sample mean of the random sample of 6189 adults . b . Construct a 95 % confidence interval for the population mean µ. Can it be concluded that the population mean is less than 2.0 ? c . On what assumptions is the analysis in part ( b ) based ? Is the assumption of randomization valid ? Is the assumption that the population distribution is approximately normal a valid assumption ? 6 . A survey asked the question “ What do you think is the ideal number of children for a family to have ?” The 473 females who responded had a median of 2 , mean of 3.13 , and standard deviation of 1.48 . Answer parts a-d . a . What is the point estimate of the population mean ? b . Find the standard error of the sample mean .