Normal Distribution as Approximation to Binomial Probability

In a binomial distribution, what is the formula used to find the mean?

• μ = n * p

• μ = n * q

• μ = q * p

• μ = n * p * q

When can we use a normal distribution to approximate a binomial distribution?

• When n is greater than 5

• When n * p is greater than or equal to 5

• When n * q is greater than or equal to 5

• When both n * p and n * q are greater than or equal to 5

In which of the following would we be able to use a normal distribution to approximate the distribution of x?

• n = 24, p = 0.85, q = 0.15

• n = 15, p = 0.70, q = 0.30

• n = 18, p = 0.90, q = 0.10

• n = 20, p = 0.65, q = 0.35

Match the following binomial probability with its corresponding normal distribution probability statement after a continuity correction.

P(x > 25)

• P(x > 25.5)

• P(x < 25.5)

• P(x > 24.5)

• P(x < 24.5)

It is know that 38% of all high school students own their own car. If I have a sample of 300 students could the probability of owning a car

be modeled with a normal distribution?

• Yes because 0.38 x 300 AND

  0.62 x 300 are both greater than 5

• Yes because 0.38 x 300 is greater than 5

• No because 0.38 is less than 0.5

• No because 0.38 + 0.62 does not equal 1.

It is known that 38% of all high school students own their own car. If I have a sample of 300 students what is the expected number of students who would NOT own their own car?

• 186

• 114

• 150

• 200

If 62% of all teenagers say they are in a relationship what is the probability that a sample 200 teenagers will have between 130 and 135 teenagers who say they are in a relationship?

• 0.109

• 0.864

• 0.5

• 0.25

If 62% of all teenagers say they are in a relationship what is the probability that a sample 200 teenagers will have fewer than 124 teenagers who will say they are in a relationship?

• 0.5

• 0.25

• 0.214

• 0.786

A student answers all 48 questions on a multiple-choice test by guessing. Each question has four possible answers, only one of which is correct. Find the probability that the student gets exactly 15 correct.

• 0.0606

• 0.0823

• 0.8577

• 0.7967

Find the probability that in 200 tosses of a fair six-sided die, a five will be obtained at least 40 times. Use the normal distribution to approximate the binomial distribution.

• 0.1210

• 0.3875

• 0.8810

• 0.7967