1. describe the characteristics of the binomial, multinomial, Poisson, and normal distributions,

2. identify the distribution of the random variable in a given problem, and

3. compute the probability of events based on its identified probability distribution.

Zia is having difficulty in deciding what Mother's Day gift she should give to

her mother. To help her decide, she conducts a series of activities.

1. Zia drew 10 cards in order from an ordinary deck of cards, returning the

card each time and if the number of red cards drawn is at most 4, she will

give her mother a 5,000 worth SM gift certificate. Otherwise, she will buy

her new kitchenware. Which gift is she likely to give her mother?

(8 points)

2. Suppose it has been observed that an average of 6 vehicles passes

by their house per minute on Wednesday mornings. One Wednesday morning, Zia counted the number of

passing vehicles. If at most 3 vehicles pass by their house in a minute, she will give her mother a new

watch. Otherwise, she will give her a necklace. What is the probability that she will choose the latter? (5

points)

3. Zia tossed a pair of fair dice 6 times. If the expected number of times that (a) a total of 7 or 11, (b) a

matching pair, and (c) any other combination occurs are all greater than 2, she will ask help from her sister.

Otherwise, she will ask help from his father. Who would she ask for help? (7 points)

4. Zia intends to buy a brand new phone with battery life that will last for more than 6 hours for her mother.

Most of her friends recommend the Iclick phone which is known to have a normally distributed battery life

(in minutes) with mean 300 minutes and standard deviation 25 minutes. If she will buy one Iclick phone,

what is the probability that its battery life is more than 6 hours? Should she proceed in buying a phone from

this brand? (5 points)