29. The randomvariable Xis binomial with parameters n= 5 and p= 0.17, compute its mean and standard deviation
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- • The expected value of x is (enter an exact decimal in 0, 1). • The variance of x is (enter a decimal rounded to the third decimal place).Suppose the number of children in a household has a binomial distribution with parameters n = 15 and p = 55%. Find the probability of a household having: (a) 11 or 13 children (b) 11 or fewer children (C) 11 or more children (d) fewer than 13 children (e) more than 11 children Be sure to give your answers to at least 4 decimal places. 業A random variable Xis binomially distributed with mean 4 and standard deviation 2.4. Find the probability that more than half the trials are successes.
- 9. Final: For recent period of 100 years, there were 530 Atlantic hurricanes. Assume the Poisson distribution is a suitable model, find the variance. O a. .3701 оь.1901 О с. 2075 O d.1016 O e. None of the above Previous pageA lot of 75 washers contains 6 defectives whose variability in thickness is unacceptably large. A sample of 10 washers is selected at random without replacement a. Find the probability that at least one unacceptable washer is in the sample b. Calculate the mean of (x) c. Calculate the standard deviation of (x)Suppose that the test score of a student taking the final of a probability course is a random variable with mean 80. (a) Give an upper bound for the probability that a student's test score will exceed 90. P{score > 90} < (b) Suppose that we know, in addition, that the variance of students' test scores on the final is 30. What can you say about the probability that a student will score between 70 and 90 (do not use the central limit theorem)? P{70 < score < 90} ? (c) How many students would have to take the final to ensure with a probability of at least 0.95 that the class average would be within 3 of 80 (do not use the central limit theorem)? n = (d) If you use the central limit theorem in (c), what is your estimate for the number of students needed? п —
- Suppose 500 people audition for admission to a dance school. Each dancer in one half of the group will be admitted with probability 0.07, while each dancer in the other half of the group will be admitted with probability 0.04. Let X be the total number of dancers admitted. (Notice that X is the sum of two binomial variables). (a) Find the mean and variance of X. (b) Use normal approximations to binomial random variables to approximate (i) the probability that more than 30 dancers are admitted. (ii) the probability that at least 20 dancers are admitted.Suppose X is a random variable with standard beta distribution and parameters (alpha) = 8 and (beta) = 2 What is (PX>=0.6)?
