3. A random variable has the following probability distribution:
A) Compute the expected value, variance, and standard deviation of X. Show the computations for each of your answers.
Fourteen percent (0.14) of the students in a statistics class are graduate students. A random sample of 10 students is selected. Use the binomial probability formula to determine the probability that the sample contains exactly 3 graduate students. Show your work.
A. what is the probability that at least 3 parts are defective?
B. what is the probability that exactly 2 parts are defective?
C. what is the expected number of defective parts in the sample?
D. What is the variance and standard deviation of defective parts in the sample?
Two letters are mailed to San Francisco. One was sent airmail, the other first-class. From past data, we know that the probability of an airmail letter arriving in 2 days is 0.55, and the probability of a first-class letter arriving in 2 days is 0.35. Assuming independence:
A. What is the probability that both letters arrive in 2 days?
B. What is the probability that at least one letter arrives in 2 days?
C. What is the probability that none of the letters arrive in 2 days?
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