Understanding Binomial Distribution

This video tutorial explains how to calculate the probability of a binomial distribution using examples such as rolling a six-sided die, answering multiple-choice questions, and selecting students taking algebra. It covers the combination formula, calculating probabilities, and determining the mean and standard deviation of a binomial distribution.

What is the probability of rolling a four exactly five times when a six-sided die is rolled 12 times?

• 28.425

• 2.8425

• 0.28425

• 0.028425

Which formula is used to calculate the probability of a specific number of successes in a binomial distribution?

• Logarithmic formula

• Exponential formula

• Combination formula

• Permutation formula

In a multiple-choice test with 20 questions, what is the probability of guessing exactly 6 questions correctly?

• 0.168609

• 168.609

• 1.68609

• 16.8609

If a student randomly guesses on a multiple-choice test with four options per question, what is the probability of guessing a question wrong?

• 0.75

• 0.5

• 0.25

• 1.0

What is the probability of selecting exactly 7 students taking algebra out of 30 chosen at random?

• 1.66236

• 166.236

• 16.6236

• 0.166236

How do you calculate the probability of fewer than 5 students taking algebra out of 30?

• Calculate for 5 and add to 1

• Calculate for 1 to 4 and sum them

• Calculate for 5 and subtract from 1

• Calculate for 0 to 5 and sum them

What is the probability of selecting fewer than 5 students taking algebra out of 30?

• 97.69

• 0.09769

• 0.9769

• 9.769

What is the mean of a binomial distribution with 30 trials and a success probability of 0.25?

• 6.5

• 8.5

• 5.5

• 7.5

How is the standard deviation of a binomial distribution calculated?

• Square root of n times p

• Square root of n times q

• Square root of n times p times q

• Square root of p times q

What is the standard deviation of a binomial distribution with 30 trials, a success probability of 0.25, and a failure probability of 0.75?

• 3.3717

• 2.3717

• 1.3717

• 4.3717