Free Printable Normal Approximation to a Binomial Distribution

1.

Under what conditions is a normal probability distribution a good approximation for a

discrete binomial distribution?

a)

np and nq greater than 5

b)

np and nq less than 5

c)

μ = np

d)

continuity correction applied

2.

For which of the binomial distributions listed below is the normal distribution not a reasonable approximation?

a)

n = 50, p = 0.4

b)

n = 40, p = 0.12

c)

n = 75, p = 0.11

d)

n = 40, p = 0.8

3.

Assuming that a normal distribution is a reasonable approximation for a binomial distribution, what value is used to approximate the mean?

a)

nq

b)

np

c)

n/p

d)

n/q

4.

Assuming that a normal distribution is a reasonable approximation for a binomial distribution, what value is used to approximate the standard deviation?

a)

npq

b)

np

c)

√np

d)

√npq

5.

QuenCola, a soft-drink company, knows that it has a 42% market share in one region of the province. QuenCola’s marketing department conducts a blind taste test with 100 people at a mall in the region. Use a normal approximation to calculate the probability that fewer than 40 of

these people will choose QuenCola.

a)

.3062

b)

.3806

c)

.6938

d)

.6914

6.

QuenCola, a soft-drink company, knows that it has a 42% market share in one region of the province. QuenCola’s marketing department conducts a blind taste test with 100 people at a mall in the region. Use a normal approximation to calculate the probability that exactly 40 of these people will choose QuenCola.

a)

.3062

b)

.6937

c)

.0743

d)

0

7.

It is estimated that 10% of the vehicles entering Canada from the United States carry undeclared goods. Use the normal approximation to calculate the probability that a search of 500 randomly selected vehicles will find more than 60 with undeclared goods.

a)

.0783

b)

.0587

c)

.0196

d)

.9412

8.

30% of all dogs in a city are micro-chipped. In a sample of 500 dogs, what is the probability that less than 140 dogs are micro-chipped? Select the closest option.

a)

0.25

b)

0.21

c)

0.15

d)

0.13

9.

A sample is taken of 200 people. The number of people who own a dog was 80.
What is the sample proportion?

a)

80

b)

0.8

c)

0.4

d)

35%

10.

Perform continuity correction for $P(x\ge4)$

a)

$P(x=4.5)$

b)

$P(x>5.5)$

c)

$P\left(x\ge3.5\right)$

d)

$P(x>4.5)$

11.

Perform continuity correction for $P(x\le4)$

a)

$P\left(x\le4.5\right)$

b)

$P(x<5.5)$

c)

$P(x<3.5)$

d)

$P(x>4.5)$

12.

Perform continuity correction for at most 20

a)

$P(x>20.5)$

b)

$P\left(x\le20.5\right)$

c)

$P(x>19.5)$

d)

$P(x<19.5)$

13.

In a city, 46 percent of the population favor the incumbent, Dawn Morgan, for mayor. A simple random sample of 500 is taken. Using the continuity correction factor, find the probability that at least 250 favor Dawn Morgan for mayor. (Write your answer as a decimal rounded to 2 decimal places)

14.

Suppose in a local Kindergarten through 12th grade (K - 12) school district, 53 percent of the population favor a charter school for grades K through 5. A simple random sample of 300 is surveyed.

Find the probability that at least 150 favor a charter school.

(Write your answer as a decimal rounded to 2 decimal places)

Normal Approximation to a Binomial Distribution

Total questions: 14

Worksheet time: 17mins

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