Probability and Continuity Corrections

The video tutorial explains how to solve a probability problem using the normal approximation to the binomial distribution. It covers identifying parameters, calculating mean and standard deviation, and applying continuity correction for probability calculations. Various examples demonstrate the approximation's accuracy compared to precise binomial calculations. The tutorial concludes with guidelines for applying continuity correction and a summary of key points.

What is the probability of success in the given problem?

• 1

• 0.75

• 0.5

• 0.25

What is the required condition for using the normal approximation?

• np and nq must be greater than or equal to 5

• np and nq must be less than 5

• n must be greater than 30

• np must be greater than nq

What is the mean of the binomial distribution in this problem?

• 15

• 20

• 10

• 5

What is the standard deviation of the binomial distribution in this problem?

• 4.0

• 1.9365

• 2.5

• 3.0

What is the continuity correction applied for calculating P(X ≤ 7)?

• P(X ≤ 7)

• P(X < 7.5)

• P(X < 7)

• P(X ≤ 7.5)

What is the approximate probability that at most 7 students drive to campus?

• 0.75

• 0.65

• 0.85

• 0.9015

What is the continuity correction applied for calculating P(X < 6)?

• P(X < 5.5)

• P(X < 6)

• P(X ≤ 5.5)

• P(X ≤ 6)

What is the approximate probability that fewer than 6 students drive to campus?

• 0.70

• 0.65

• 0.55

• 0.6026

What is the continuity correction applied for calculating P(X > 3)?

• P(X > 3.5)

• P(X ≥ 3.5)

• P(X > 4)

• P(X ≥ 4)

What is the approximate probability that more than 3 students drive to campus?

• 0.85

• 0.70

• 0.7794

• 0.80