The mean number of carats for 320 diamonds in a sample data

The mean number of carats for 320 diamonds in a sample data set is 0.635 carats, with a standard deviation of 0.274 carats. Use the mean and standard deviation to form an interval that will contain at least 75% of the carat values in the data set. At least 75% of the carat values in the data set are between and carats. (Round to three decimal places as needed.)

Solution

Mean = 0.635 and std dev = 0.274, n =320

75% z value = 1.13

Hence confidence interval = (0.635-1.13(0.274/rt320), 0.635-1.13(0.274/rt320))

= (0.635-0.0173, 0.635+0.0173)

= (0.618,0.652)