Essay About Binomial Distribution And Normal Distribution

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1. For each question below indicate True (T) or False (F)
a. The binomial distribution is a possible model for a continuous variable: F
b. In any normal distribution 95% of the probability lies within two standard deviations of the mean: T
c. For a Poisson(m=4) distribution the variance is 2: F
d. For any exponential distribution, the mean is greater than the median: T
e. 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?
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):
(value) (value)
(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, whats the probability that in 2 weeks there will
be only one accident? Let X be the number of accidents in 2 weeks.
Prob. Statement value
(show work: Hint: whats 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: