Q2. Suppose the height of new born girl baby follows a normal distribution with mean height of 50cm, standard deviation of 3cm.

1. Find the probability that one randomly selected new born girl baby's height is less than 45cm.

2. For two independently selected new born girl babies. Find the probability that both height is less than 45cm.

Q3. In a grocery store, for customers who purchased tomato, let X be the number of purchased tomato for one randomly selected customer, the probability distribution for X is given below:

X	1	2	3	4
P(X)	0.1	0.5	0.2	0.2

1. Suppose two customers who purchase tomato are randomly selected. Find the probability distribution for the sample mean number of tomato purchased, X.
2. Find the mean, variance, and standard deviation of X

Q4. The average number of serious accidents occurred on one highway is 2.1 per week. Assume the number of serious accidents is independent from week to week. Let XX be the number of serious accident in one randomly selected week.

1. Find the mean and variance for XX.

2. Find the probability that the number of serious accidents is exactly three in this randomly selected week.

3. Find the probability that the number of serious accident is greater than two and less than six, in this randomly selected week.

Q5. Calculate the following probabilities.

1. ZN(0,1),P(Z>1.54)ZN(0,1),P(Z>1.54).

2. XN(2,42),P(0.4X1.6)XN(2,42),P(0.4X1.6).

3. XN(3,72),P(X<1.54)XN(3,72),P(X<1.54).