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1. For each question at a lower place indicate True (T) or False (F)a. The binomial distribution is a bunkable model for a continuous unsettled Fb. In any normal distribution 95% of the probability lies within ii standard deviations of the mean value 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. minded(p) that the area under(a) the standard normal curve, to the left of 2.3 is .0107, what is the areaunder 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 followingprobabilities (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 vex it isknown that on an average there are 5 accidents per week. presume that the number of accidents inany week follows a Poisson distribution with mean 5, whats the probability that in 2 weeks there willbe totally one accident? Let X be the number of accidents in 2 weeks.______P(X=1)________________ __10*e-10__________Prob. Statement value(show work Hint whats the distribution of X?)XPoisson(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. Thescore distribution is shown in practice 1 below. Answer the following questions. Let X denote thevariable score.(a) Refer to the blue shaded area in figure 1. This is the probability of__P(X 70)______________ (just spell out the probability statement).(b) Find the value of probability in part (a) (show work)_P(Z