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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)______________ (just write the probability statement). (b) Find the value of probability in part (a) (show work) _P(Z