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- B is 4The distance between major cracks in a high way follows an Exponential distribution with a mean of five miles (μ=5 and λ=0.2/mile). What is the distribution of the number of major cracks within 10 miles in a high way? [*hint: the relationship between Exponential and Poisson Distribution] a). Poisson with λ=2 b). Poisson with λ=1 c). Poisson with λ=10 d). cannot be determinedAssume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.75 probability that a pea has green pods. Assume that the offspring peas are randomly selected in groups of 24. Complete parts (a) through (c) below. a. Find the mean and the standard deviation for the numbers of peas with green pods in the groups of 24. The value of the mean is muμequals= peas. (Type an integer or a decimal. Do not round.) The value of the standard deviation is sigmaσequals= peas. (Round to one decimal place as needed.) b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high. Values ofpeas or fewer are significantly low. (Round to one decimal place as needed.) Values of nothing peas or greater are significantly high. (Round to one decimal place as needed.) c. Is a result of 11 peas with green pods a result that is significantly low? Why or why not? The result ▼ is…
- only need d,e,f) Determine the mean (μ!" ) of sample means distribution (x#-distribution).b) Determine the standard deviation (standard error) (σ!" ) of sample means distribution(x#-distribution).c) Draw a Normal (bell-shaped) graph for sample means distribution (x#-distribution) byhand on a paper showing x and y axes without any values marked on them. However,label the values of mean and standard deviation as described below. The adult male heights in a country vary normally with mean of 70 inches and standarddeviation of 4 inches. We draw many samples of size 100 from the above populationusing repeated random sampling and record the mean height for each sample to constitutea sample means distribution (x#-distribution). Do the above for the distribution.The moment generating function of the negative binomial distribution is given by m,)-ge pe' . Derive the mean of the distribution using the mgf. 1- qe'
- True/False a)It is appropriate to use A Normal approximation for a Binomial distribution with n=15 and p=0.2. b)Both the Hypergeometric and the Binomial distributions deal with dichotomous (binary) data.6) Suppose the m.g.f. of the r.v. X is given below: MCA) = (uM/ R0) +(45 |no) exp (t) A(20/1201eapreb a) Find the mean and variance of X b) Find P(X>1)Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)
- 3. For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation. n= 65 and p = 0.7 a. Normal approximation is not suitable. b. Normal approximation is suitable.1 find the first four moments of the binomial distribution 9. Ifx is a binomial variate with parameters 6 and 2 about origin.Under what conditions will you use the Poisson and Binomial distributions?