a. P(X = 3) when n = 5 and π = 0.5
b. P(X = 1) when n = 4 and π = 0.7
c. P(X = 5) when n = 10 and π = 0.3
2. Use the Binomial Distribution tables to find the following probabilities:
a. P(X = 5) when n = 7 and π = 0.5
b. P(X = 4) when n = 10 and π = 0.6
c. P(X < 3) when n = 5 and π = 0.15
3. It is known that 20% of households have a dog.

4. Light bulbs are tested for their lifespan. It is found that 4% of the light bulbs are rejected. A random sample of 15 bulbs is taken from stock and tested. The random variable X is the number of bulbs that a rejected.
a. Give four reasons why X will have a binomial distribution.
b. Use a formula to find the probability that 2 light bulbs in the sample are rejected.
5. Based on previous results a marksman firing at a target hits the bull's eye with one in every four shots. If he fires at the target 7 times what is the probability that he will hit the bull's eye:

6. If 95% of households have a TV and 8 houses are surveyed, what is the probability that more than 6 have a TV?
7. A manufacturer knows that an average of 1 out of 10 of his products are faulty.
What is the probability that a random sample of 5 articles will contain:
a. No faulty products
b. Exactly 1 faulty products
c. At least 2 faulty products
d. No more than 3 faulty products
8. Complete the table for the following binomial distributions:
n

π

mean

variance

standard deviation


a

50

0.5


b

20

5


c

0.4

100

where n = number of trials and π = probability of a success.
9. If the probability that it is a rainy day is 0.3, find the mean number of rainy days in a week and the standard deviation.
10. In a packet of flower seeds 30% are known to produce red flowers and the remainder produce white flowers.
X is the number of red flowers in a row of 5 plants,
a. Copy and complete the following probability table. (Round values to 2 decimal places.)
x

0

1

2

3

4

5

P(X = x)

0.17

b. Use the table to find E(X) and VAR(X) .c. Use the binomial distribution formulae to check these results.
11. The probability that cars passing a speed camera are speeding is 0.23. If 750 cars pass the camera, how many of the cars would you expect to be speeding and what would be the standard deviation?