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Three performers are invited to an audition. Assume all three performers arrive on their own. Here, the
(a) How do I find the distribution (pmf) of X?
(b) How would I calculate the
Identify the random variable: In this problem, the random variable is X, which represents the number of late participants among the three performers.
Determine the probability of success and failure: You are given that the probability of any one performer being late is 0.2, so p (probability of success) is 0.2, and (1 - p) is the probability of not being late, which is 0.8.
Recognize the binomial distribution: Since each performer's lateness is independent, and you want to find the probability distribution of the number of late performers out of a fixed number of trials (in this case, 3 trials), you can use the binomial distribution.
Calculate the probability mass function (pmf): Use the binomial distribution formula to calculate the probabilities of different values of X (the number of late participants) for k = 0, 1, 2, and 3.
- Since the distribution is binomial.
Formulae for mean and variance of X:
E(X) = np ; n -> number of trials ; k = 0,1,...,n ; here n = 3
Var(X) = np(1-p)
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- You run a candle manufacturing factory and over the past year the average output of the factory is 480 candles per day and the standard deviation is 10 candles per day. You plan to select 39 upcoming days at random and measure the outputs on those days. Then you will calculate the mean output in the sample of 39 days. What is the probability that the sample mean output will be within 3 candles of the population mean? z= ((x ̅- μ))/(s/√n) I got the probability is equal to 0.971. Is that correct?arrow_forwardLet x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean ? = 70.0 kg and standard deviation ? = 7.6 kg. Suppose a doe that weighs less than 61 kg is considered undernourished. (c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 45 does should be more than 67 kg. If the average weight is less than 67 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x for a random sample of 45 does is less than 67 kg (assuming a healthy population)? (Round your answer to four decimal places.)(d) Compute the probability that x< 71.8 kg for 45 does (assume a healthy population). (Round your answer to four decimal places.)arrow_forwardHow would you figure out this problem for (a,b,c,d)?arrow_forward
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- You decided to plant roses. The probability that a planted roses seedgerminates is 0.80. You plant nine seeds and let the binomial random variable X denotes the number ofroses seeds that successfully germinate. What is the average number of roses you could expect togerminate? What is the variance and standard deviation of X?arrow_forwarda, b, d,arrow_forwardrefer to the photoarrow_forward
- A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
