Understanding Binomial Distribution in Quality Control

The video tutorial explains how to calculate the mean and standard deviation of defective processing chips in a sample of 500 chips. It defines the random variable X as the number of defective chips and identifies it as a binomial variable. The tutorial walks through the formulas for calculating the mean and standard deviation, assuming a constant probability of defectiveness and independent trials.

What percentage of the processing chips produced by the company are defective?

• 1%

• 2%

• 10%

• 5%

How many chips are randomly selected for the quality check?

• 250

• 1000

• 100

• 500

What type of random variable is used to model the number of defective chips?

• Normal

• Binomial

• Poisson

• Exponential

Why is the defective chip considered a 'success' in this context?

• Because it is the only possible outcome

• Because it is the desired result

• Because it is the event being counted

• Because it is a positive outcome

What is the formula used to calculate the mean of a binomial variable?

• n - p

• n / p

• n + p

• n * p

What is the expected number of defective chips in the sample?

• 5

• 20

• 10

• 15

What is the formula for the variance of a binomial variable?

• n * p * (1 - p)

• n + p * (1 - p)

• n - p * (1 + p)

• n / p * (1 + p)

What is the approximate standard deviation of the number of defective chips?

• 3.13

• 4.0

• 2.5

• 5.5

If the variance of the defective chips is 9.8, what is the standard deviation?

• 4.5

• 3.5

• 4.0

• 3.13

What is the variance of the number of defective chips in the sample?

• 8.5

• 11.5

• 9.8

• 10.2