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Mathematics
11th -
12thgrade
Section 5.5: Normal Approximation to the Binomial Distribution
11 questions
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- 1. Multiple Choice
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
- 2. Multiple Choice
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
- 3. Multiple Choice
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
- 4. Multiple Choice
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)
- 5. Multiple Choice
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.
- 6. Multiple Choice
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
- 7. Multiple Choice
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?
0.165
0.864
0.5
0.25
- 8. Multiple Choice
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?
0.4710
0.25
0.214
0.786
- 9. Multiple Choice
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
0.0807
0.8577
0.7967
- 10. Multiple Choice
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
- 11. Multiple Choice
A telemarketer found that there was a 1% chance of a sale from his phone solicitations. Find the probability of getting 5 or more sales for 1000 telephone calls. Use the normal distribution to approximate the binomial distribution.
0.0871
0.8810
0.9599
0.0401
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