A company manufactured 1,000 televisions. Testing showed that 20 of the televisions were defective.
PART A: What is the experimental probability that the next television will be defective?
PART B: Based on the probability in PART A, how many of the next 5,000 televisions manufactured should the company expect to be defective?
A) prob = 20/1000 =1/50
b) number expected to be defective = (1/50)(5000)
= 100
10
To answer these questions, we need to understand experimental probability and how it can be calculated.
PART A:
The experimental probability is the ratio of the number of favorable outcomes (defective televisions) to the total number of outcomes (total televisions manufactured).
We are given that out of the 1,000 televisions manufactured, 20 were defective. Therefore, the experimental probability of the next television being defective is:
Number of favorable outcomes / Total number of outcomes = 20/1000 = 0.02
So, the experimental probability that the next television will be defective is 0.02 or 2%.
PART B:
Based on the probability calculated in PART A, we can use it to estimate the number of televisions we can expect to be defective out of the next 5,000 manufactured.
We know that the experimental probability of a television being defective is 0.02 or 2%. Therefore, for every 100 televisions manufactured, we can expect 2 to be defective.
To find the expected number of defective televisions out of the next 5,000 manufactured, we can set up a proportion:
(2 defective / 100 televisions) = (x defective / 5,000 televisions)
By cross-multiplying, we get:
(100 * x) = (2 * 5,000)
100x = 10,000
x = 10,000 / 100
x = 100
Hence, the company should expect approximately 100 of the next 5,000 televisions manufactured to be defective.