Question

Suppose that 1 out of 4 eggs contain the Salmonella virus, and eggs are independent of each other with regard to having Salmonella. If Sue uses 3 eggs to bake a cake, the distribution describing the probability of getting eggs with the virus is

		binomial, with n = 4 and p=1/3
		binomial, with n = 3 and p = 1/3
		binomial, with n = 3 and p= 1/4
		not binomial

Which of the following is a characteristic of the binomial distribution?

		The probability changes from trial to trial
		The outcome of each trial depends on the outcome of the previous trial
		Each trial typically has 3 outcomes
		The probability of success is constant, trial to trial

A coin is weighted so that it turns up heads 60% of the time. If the coin is flipped 10 times, and the flips are independent of each other, the distribution is

		binomial, with n = 60 and p = 1/10, or 0.1
		binomial, with n = 10 and p = 0.6
		binomial, with n = 10 and p = 1/2, or 0.5
		not binomial

Which of the following is not a characteristic of a binomial distrIbution?

		2 and only 2 outcomes per trial
		At least 3 outcomes per trial
		The probability of success does not change from trial to trial
		The outcome of a trial does not affect the outcome of the next trial

As the number of trials gets large, a binomial distribution starts to resemble a

		Right-skewed distribution
		uniform distribution
		normal distribution
		linear regression line

In order for n to be large enough for the normal distribution to be able to approximate the binomial, n must be

a. np > 10

b. np > 10 and n(1-p) > 10

c. n > 100

d. n > 100 and p > 0.1

Answer 1

Answer to 1st question :

Probability of an egg containing the Salmonella Virus = 1 / 4

Given , Sue uses 3 eggs to bake.

Let X be a random variable representing the number of eggs that contain the Salmonella virus

Therefore , X follows Binomial Distribution with parameters n = 3 and p = 1/4

Hence , 3rd Option is correct

Answer to 2nd question :

In a Binomial Distribution , the probability of success does not change from trial to trial. It remains constant

Hence , 4th Option is correct

Answer to 3rd question :

Probability of getting a head = 60/100 = 0.6

Let Y be a random variable representing the number of heads in 10 flips of a coin

Therefore , Y follows Binomial Distribution with parameter n = 10 and p = 0.6

Hence , 2nd Option is correct

Answer to 4th question :

In a single trial of a Binomial experiment there can only be two possible outcomes and one single outcome

Hence , 2nd Option is correct as it is not a characteristic of Binomial Distribution.

Answer to 5th question :

3rd Option is correct, as the number of trials increases the binomial distribution starts to resemble a Normal Distribution.

Answer to 6th question :

The number of observations n must be large enough, and the value of p so that both np and n(1 - p) are greater than or equal to 10 , for a binomial to resemble a normal distribution.

Hence , 2nd Option is correct