The Early Morning Delivery Service guarantees delivery of small packages by 10:3

Question

The Early Morning Delivery Service guarantees delivery of small packages by 10:30 A.M. Of course, some of the packages are not delivered by 10:30 A.M. For a sample of 200 packages delivered each of the last 15 working days, the following number of packages were delivered after the deadline:

9, 14, 2, 13, 9, 5, 9, 3, 4, 3, 4, 3, 3, 8, and 4.

(a) Determine the mean proportion of packages delivered after 10:30 A.M.

(b) Determine the control limits for the proportion of packages delivered after 10:30 A.M. Were any of the sampled days out of control?

(c) If 10 packages out of 200 in the sample were delivered after 10:30 A.M. today, is this sample within the control limits?

Explanation / Answer

a) Mean = 1/15 *(9+14+2+13+9+5+9+3+4+3+4+3+3+8+4) = 93/15 = 6.2

b)standard deviation = 3.72

so that shows sampled days are within the control limits

c) Mean = 93+10/16 = 6.066

std dev = 3.72

sample within the limits

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