Question

A company manufactures 2,000 units of its flagship product in a day. The quality control department takes a random sample of 40 units to test for quality. The product is put through a wear-and-tear test to determine the number of days it could last. If the product has a lifespan of less than 26 days, it is considered defective. The table gives the sample data that a quality control manager collected.
39 31 38 40 29
32 33 39 35 32
32 27 30 31 27
30 29 34 36 25
30 32 38 35 40
29 32 31 26 26
32 26 30 40 32
39 37 25 29 34

The point estimate of the mean of the sample is _____, and the point proportion of the defective units is _______.
(Give your answers as decimal numbers rounded off to the nearest hundredth.)

Answer 1

Mean | $32.3$

Median | $32$

Sample Standard Deviation | $4.49$

$5$

Numerical Order:

$25,25,26,26,26,27,27,29,29,29,29,30,30,30,30,31,31,31,32,32,32,32,32,32,32,33,34,34,35,35,36,37,38,38,39,39,39,40,40,40$

Answer 2

The point estimate of the mean of the sample is (39 + 31 + 38 + 40 + 29 + 32 + 33 + 39 + 35 + 32 + 32 + 27 + 30 + 31 + 27 + 30 + 29 + 34 + 36 + 25 + 30 + 32 + 38 + 35 + 40 + 29 + 32 + 31 + 26 + 26 + 32 + 26 + 30 + 40 + 32 + 39 + 37 + 25 + 29 + 34) / 40 = 1292/40 = 32.30

The point proportion of defective units is 2/40 = 0.05