7.42 Counts of picks in a one-pound bag. A guitar supply company must maintain strict oversight on the number of picks they package for sale to customers. Their current advertisement specifies between 900 and 1000 picks in every bag. An SRS of 36 one-pound bags of picks was collected as part of a quality improvement effort within the company. The number of picks in each bag is shown in the following table.

924 925 967 909 959 937 970 936 952
919 965 921 913 886 956 962 916 945
957 912 961 950 923 935 969 916 952
917 977 940 924 957 920 986 895 923

  1. (a) Create (i) a histogram or stemplot, (ii) a boxplot, and (iii) a Normal quantile plot of these counts. Write a careful description of the distribution. Make sure to note any outliers, and comment on the skewness and Normality of the data.

  2. (b) Based on your observations in part (a), is it appropriate to analyze these data using the t procedures? Briefly explain your response.

  3. (c) Find the mean, the standard deviation, and the standard error of the mean for this sample.

  4. (d) Calculate the 90% confidence interval for the mean number of picks in a one-pound bag.