## Binomial Distribution Exercise

1. Use the Combination tables and binomial formula to find the following probabilities:

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.If 10 houses are chosen at random, what is the probability that: a. Three will have a dog (use the formula) b. No more than three will have a dog. (use tables)

4. Light bulbs are tested for their life-span. 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: a. Four timesb. Neverc. At least five times 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?