Suppose for a certain microRNA of size 20, the probability of getting a purine is binomially distributed with a probability of 0.7. There are 100 of these microRNAs, each independent of the other. Let Y denote the average number of purine in these microRNAs. Find the probability that Y is greater than 15.
Y follows Binomial (100, 0.7)
P(Y=y) = 100Cy * 0.7y * 0.3100-y
P(Y>15) = Sum all values of y from 16 to 100 over P [Y=y)
P(Y>15) = 0.999999
Suppose for a certain microRNA of size 20, the probability of getting a purine is binomially...
Suppose that the probability that a certain experiment will be successful is 0.4, and let X denote the number of successes that are obtained in 15 independent trials of the experiment. A. What is the probability that there will be between 6 and 9 successes? B. What is the expected number of successes? C. What is the variance? D. Suppose the scientists decide to re-run the experiment 250 times. What is the probability that the number of success will be...
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2. Suppose that 10% of all steel shafts produced by a certain process are nonconforming but can be re- worked (rather than having to be scrapped). Consider a random sample of 200 shafts, and let X denote the number among these that are nonconforming and can be reworked. What is the (approximate) probability that X is a) At most 302 (2) b) Between 15 and 25 (both inclusive)? [2] c) Assume that the probability of at most x shafts being...
2. Suppose that 10% of all steel shafts produced by a certain process are nonconforming but can be re- worked (rather than having to be scrapped). Consider a random sample of 200 shafts, and let X denote the number among these that are nonconforming and can be reworked. What is the approximate) probability that X is a) At most 30? [2] b) Between 15 and 25 (both inclusive)? [2] c) Assume that the probability of at most x shafts being...