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1. For each question below indicate confessedly (T) or False (F)a. The binomial distribution is a possible personate for a continuous variable Fb. In every approach pattern distribution 95% of the opportunity lies within two commonplace deviations of the designate 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 adept approximation to binomial when n is large and p is small. T(2+2+2+2+2=10 points)2. Given that the celestial sphere beneath the standard normal arch, 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 cash 7 times, let X be the possible number of heads. watch 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. rumor _P(X > 2)__ value __1-(.5)7-7*(.5)7___(5+5+7+5=22 points)4. You are the safety inspector at some part manufacturing plant. Safety at the plant is a concern it isknown that on an average there are 5 possibilitys per week. Assuming that the number of accidents inany week follows a Poisson distribution with mean 5, whats the probability that in 2 weeks there willbe 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 whats the distribution of X?)XPoisson(mean=2*5=10) (8+7=15 points)5. The scores on a foot race are normally distributed with a mean of 80 and a standard deviation of 5. Thescore distribution is shown in figure 1 below. execute the following questions. Let X denote thevariable score.(a) Refer to the blueness shaded area in figure 1. This is the probability of__P(X < 70)______________ (just write the probability statement).(b) discern the value of probability in pa rt (a) (show work)_P(Z<-2) = .0228__________(c) Whats the probability of scoring among 70 and 80?(i) Draw the picture Label and Shade the area to indicate the required area.P(70<X<80) =P(-2<Z<0)=.5-.0228=.4772 --- DTDP(ii) The value of the required probability in (i) is _______.