M&M candies large candy bags have a claimed net weight of 396.9 g. The standard deviation for the weight of the individual candies is 0.017 g. The following table is from a stats experiment conducted by a statistics class.

Red Orange Yellow Brown Blue Green

0.771 0.735 0.883 0.706 0.881 0.925

0.841 0.895 0.789 0.876 0.863 0.914

0.856 0.865 0.859 0.855 0.775 0.881

0.799 0.864 0.784 0.806 0.854 0.865

0.966 0.852 0.844 0.840 0.810 0.865

0.859 0.866 0.858 0.868 0.858 1.015

0.857 0.859 0.848 0.859 0.818 0.876

0.942 0.838 0.851 0.982 0.868 0.819

0.873 0.863 0.803 0.865

0.809 0.888 0.932 0.848

0.890 0.925 0.842 0.940

0.878 0.793 0.832 0.833

0.905 0.967 0.827 0.845

0.854 0.850 0.841 0.852

0.830 0.932 0.798

0.856 0.833 0.814

0.842 0.881 0.791

0.778 0.818 0.810

0.786 0.864 0.881

0.853 0.825

0.864 0.855

0.873 0.942

0.880 0.825

0.882 0.869

0.931 0.922

0.887

The bag contained 465 candies and the listed weights in the table came from randomly selected candies. Count the weights.

Find the mean sample weight and the standard deviation of the sample weights of candies in the table. (Round your answers to five decimal places.)

mean ____________

standard deviation_____________

Part (b)

Find the sum of the sample weights in the table and the standard deviation of the sum of the weights. (Round your answers to three decimal places.)

sum___________________

standard deviation_____________

Part (c)

If 465 M&Ms are randomly selected, find the probability that their weights sum to at least 396.9. (Round your answer to four decimal places.)

__________