A quality control inspector found flaws in 13 out of 150 sweaters. Find the probabillity that a sweater has a flaw. Round to nearest tenth of a %
But what if the company produces 500 sweaters, how many will NOT have flaws
150 - 13 = 137 without flaws
137 * (500/150) = 457
this is simplistic. The chances are that around 457 do not have flaws based on our sample of 137 out of 150 flaw free. You of course can not say for sure.
connections accadamy huh
To find the probability that a sweater has a flaw, we need to divide the number of flawed sweaters by the total number of sweaters.
Given:
Number of flawed sweaters = 13
Total number of sweaters = 150
Therefore, the probability is calculated as:
Probability = (Number of flawed sweaters) / (Total number of sweaters)
= 13 / 150
≈ 0.0867
To round to the nearest tenth of a percent, we need to multiply the probability by 100 and round to the nearest tenth.
Probability ≈ 0.0867 * 100 ≈ 8.7%
Now, let's address the second part of your question:
If the company produces 500 sweaters, and the probability of a sweater having a flaw is 8.7%, we can calculate the expected number of flawed sweaters by multiplying the probability by the total number of sweaters:
Expected number of flawed sweaters = (Probability) * (Total number of sweaters)
= 0.087 * 500
= 43.5
Rounding to the nearest whole number, we can expect around 44 sweaters to have flaws. Therefore, the number of sweaters without flaws would be the difference between the total number of sweaters and the number of flawed sweaters:
Number of sweaters without flaws = Total number of sweaters - Number of flawed sweaters
= 500 - 44
= 456
So, if the company produces 500 sweaters, approximately 456 sweaters will not have flaws.