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Question No. 1
A box contains 4 red and 5 white flowers. A random sample of 6 flowers is drawn without replacement from the box. Find the probability that the sample contains 3 red flowers.
Given Data: N=9 n=6 k=3 p=?
Applying the Formula:
Putting the Values If X is binomially distributed with mean 8 and variance 4.8, then find the parameters of binomial distribution. Solution (b): Given data: Mean: 8 Variance: 4.8 Find Parameters of Binomial Distribution “n” and “p” ? Hence, Applying the Formula: P = 0.4 Question No. 2 Suppose the number of defective screws produced by a machine per day follows Poisson distribution with parameter 2. What is the probability that, out of the total production of the day, there are at least one defective screw? Solution (a): Let suppose the X be the number of defective screws produced in a day. Hence: k = 0,1,2,3,…. The Army reports that the distribution of head circumferences among soldiers is approximately normal with mean 23.4 inches and standard deviation 1.4 inches. What percent of soldiers have a head circumference between 21.0 inches and 24.0 inches? Solution (b): X = Head circumference; with X ~ N(23.4, 1.4) Given: P(21.0 < X < 24.0) = 0.6228
STA301 GSB Solution