1. For each question below indicate True (T) or False (F) a. The binomial distribution is a possible model for a continuous variable: Fb. In any normal distribution 95% of the probability lies within two standard deviations of the mean: Tc. For a Poisson (m = 4) distribution the variance is 2: Fd. For any exponential distribution, the mean is greater than the median: Te.
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) D TDP 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) ( ) 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 95) = P (Z 3) = P (Z.