A random variable follows a binomial distribution with a probability of success equal to 0.68. For a sample size of n=8, find:- 1.The probability of exactly 3 success 2.The expected value(mean) 3.The variance of the random variable

76% of U.S. adults think that political correctness is a problem in America today. You randomly select six U.S. adults and ask them whether they think that political correctness is a problem in America today. The random variable represents the number of U.S. adults who think that political correctness is a problem in America today. Answer the questions below. 1.mean of the binomial distribution 2.variance of the binomial distribution 3.standard deviation

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Service time for a customer coming through a checkout counter in a retail store is a random variable with the mean of 4.0 minutes and standard deviation of 2.0 minutes. Suppose that the distribution of service time is fairly close to a normal distribution. Suppose there are two counters in a store, n₁ = 46 customers in the first line and n₂ = 52 customers in the second line. Find the probability that the difference between the mean service time for the shorter line X₁ and the mean service time for the longer one X₂ is more than 0.3 minutes. Assume that the service times for each customer can be regarded as independent random variables. Round your answer to two decimal places (e.g. 98.76). P = !

ABC Builder decides to apply a veneer to an external part of the building in order to protect it from erosion. If the density of the veneer follows a uniform distribution between 12 and 24 microns, determine:  the mean density of the veneer of the protective building  The standard deviation of the density of the protective building  The probability that the protective building is between 15- and 20-microns dense  The probability that the protective building is less than 22 microns dense.

Determine the standard deviation of the random variable, B(600,0.4).