C++

1. For each question below indicate True (T) or False (F)

a. The binomial distribution is a possible model for a continuous variable: F

b. In any normal distribution 95% of the probability lies within two standard deviations of the mean: T

c. For a Poisson(m=4) distribution the variance is 2: F

d. For any exponential distribution, the mean is greater than the median: T

e. The Poisson is a good approximation to binomial when n is large and p is small. T

(2+2+2+2+2=10 points)

2. Given that the area under the standard normal curve, to the left of -2.3 is .0107, what is the area

under the normal curve to the right of 2.3?

(show work) DTDP ____0.0107____________

value

(8 points)

3. Suppose you flip a fair coin 7 times, let X be the possible number of heads. Find the following

probabilities (in each case show work below):

(i) P(X = 0) =___(.5)7______________ (ii) P(X = 1) = __7*.5*.56_________

(value) (value)

(iii) Probability of at least 2 heads: Prob. Statement: _P(X > 2)__ value __1-(.5)7-7*(.5)7___

(5+5+7+5=22 points)

4. You are the safety inspector at some parts manufacturing plant. Safety at the plant is a concern; it is

known that on an average there are 5 accidents per week. Assuming that the number of accidents in

any week follows a Poisson distribution with mean 5, what's the probability that in 2 weeks there will

be only one accident? Let X be the number of accidents in 2 weeks.

______P(X=1)________________ __10*e-10__________

Prob. Statement value

(show work: Hint: what's the distribution of X?)

X~Poisson(mean=2*5=10) (8+7=15 points)

5. The scores on a test are normally distributed with a mean of 80 and a standard deviation of 5. The

score distribution is shown in figure 1 below. Answer the following questions. Let X denote the

variable score.

(a) Refer to the blue shaded area in figure 1. This is the probability of:

__P(X < 70)______________