Normal Distribution as Approximation to Binomial Probability

Under what conditions is a normal probability distribution a good approximation for a discrete binomial distribution?

• np and nq greater than 5

• np and nq less than 5

• μ = np

• continuity correction applied

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

• n = 50, p = 0.4

• n = 40, p = 0.12

• n = 75, p = 0.11

• n = 40, p = 0.8

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

• nq

• np

• n/p

• n/q

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

• npq

• np

• √np

• √npq

In which of the following situations would it be appropriate to use a Normal distribution to approximate probabilities for a binomial distribution with the given values of n and p?

• n = 10, p = 0.5

• n = 40, p = 0.88

• n = 100, p = 0.2

• n = 100, p = 0.99

• n = 1000, p = 0.003

The mean number of accidents a week at a company is 6.4 with a standard deviation of 1.5.  What proportion of weeks would you expect to have more than 7 accidents?

• 0.3446

• 0.2856

• 0.4

• 0.6554

What is the condition to get approximate normal distribution from a binomial distribution?

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.

• .3062

• .3806

• .6938

• .6914

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.

• .3062

• .6937

• .0743

• 0

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.

• .0783

• .0587

• .0196

• .9412