Find the area under the standard normal curve that lies (a) between x = -1.0 and

Question

Find the area under the standard normal curve that lies (a) between x = -1.0 and z = 1.0; (b) to the right of z = -2.0. (c) to the left of z = 3.0; (d) between x = -4.0 and z = 4.0. Find the mean and the variance of the binomial distribution with P = 0.20 (a) by looking up the probabilities in Table I and then using the formula for the mean and the variance of a probability distribution (b) by using the special formulas for the mean and the variance of the distribution. Check in each case whether the conditions given in Section 6.4 for the approximation to the binomial distribution are satisfied: (a) n = 150 and p = 1/10; (b) n = 450 and p = 1/50; (c) n = 600 and p = 1/100. A certain type of rope used for nautical purposes lasts, on the average, 36 months, with a standard deviation of 6.0 months. Find the probability that a randomly selected coil of this rope will last, on the average, at least 30 months. The correction is not required in this exercise. Suppose that the number of computers sold each day by a computer store is a random variable with mu = 30 computers and sigma = 5 computers. Find the probability that on a certain day (a) more than 36 computers will be sold; (b) fewer than 24 computers will be sold; (c) between 24 and 36 computers, inclusive, will be sold. Use the continuity correction in this exercise. A zoo has a large primate collection including eight baboons and six chimpanzees. If a veterinarian randomly picks four of them for examination, what are the probabilities that these will include (a) two baboons and two chimpanzees; (b) one baboon and three chimpanzees? Use Table X, Binomial Coefficients, to determine (a) how many random samples of size 3 can be drawn from a finite population of 12. (b) Using the result of part (a), what is the probability of each sample? In each case, determine whether the given values can be looked upon as the values of a probability distribution of a random variable that can take on the values 1, 2, 3, 4, and 5, and explain your answers: (a) f(1) = 0.18, f(2) = 0.20, f(3) = 0.22, f(4) = 0.20, f(5) = 0.18; (b) f(1) = 0.05, f(2) = 0.05, f(3) = 0.05, f(4) = -0.05, f(5) = 0.90; (c) f(1) = 0.07, f(2) = 0.23, f(3) = 0.50, f(4) = 0.19, f(5) = 0.01.

Explanation / Answer

97)

b)

Distribution of x is binomial with parameters

n=6 and p=0.20

mean=np

mean=4*0.20

mean=0.8

variance=npq

where q=1-p

q=1-0.2

q=0.8

variance=0.64

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