Question

A store receives a shipment of 5,000 mp3 players. in a previous shipment of 5,000 mp3 players, 300 were defective. a store clerk generates random numbers to simulate a random sample of this shipment. the clerk lets the numbers 1 through 300 represent defective mp3 players, and the numbers 301 through 5,000 represent working mp3 players. the results are given. 2,286 448 266 4,996 1,475 501 3,879 60 916 453 based on this sample, how many of the mp3 players might the clerk predict would be defective?

Answer 1

The number of defective mp3 players predicted by clerk are:

1000

Explanation:

A store receives a shipment of 5,000 mp3 players out of which 300 were found to be defective.

The clerk lets the numbers 1 through 300 represent defective mp3 players, and the numbers 301 through 5,000 represent working mp3 players.

The results are given AS:

2,286 448 266 4,996 1,475 501 3,879 60 916 453

This means that out of the 10 samples 2 were found to be defective and 8 were in the working condition.

( Since the number 266 and 60 represent the defective mp3 players as they are the numbers which are less than or equal to 300 )

Hence, the Probability that the mp3 players were defective is:

P( defective)=2/10=1/5

Hence, out of 5000 mp3 players the number of players that clerk predict to be defective are:

P( defective)×5000

=1/5×5000

=1000.

Hence, the clerk predicts that the defective number of mp3 players are:

1000

Answer 2

Numbers less than 300 = 2
Total numbers = 10

Percentage defective = 2/10 x 100 = 20%

Expected defective pieces = 5,000 x 0.2
Expected defective pieces = 1,000