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- -5. The weight of a certains species of fish is normally distributed with mean of 4.25 Kg and standard deviation of 1.2 a) What proportion of fish are between 3.5 kg and 4 kg b) What is the probability that a fish caught will have a weight of at least 5kg? 318) a) In simple words describe the median, dos, of the probability distribution for a continuous random variable Y. b) Write the median for a random variable with uniform distribution on the interval [a,b]. c) Write the median for a normal distribution with mean u and standard deviation o. d) Find the median for an exponential distribution with mean ß.The length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviation of 2 months. Find the probability that an instrument produced by this machine will last a.) less than 8 months b.) between 8 and 12 months.
- Assume that X has a normal distribution, and find the indicated probability. 7) The mean is μ = 15.2 and the standard deviation is o = 0.9. Find the probability that X is between 14.3 and 16.1. A) 0.1587 B) 0.6826 C) 0.8413 D) 0.3413 7)13) For a random variable with mean=10 and standard deviation=2, (show work) a. Find the value that corresponds to z-score=-2.4. b. applying Chebeche's Rule, find value of k such that at least 60% of the measures are within k standard deviation of the mean.Let the weights of 1 kg tea boxes filled with an automatic machine have a normal distribution with a mean of μ=1.03 and a standard deviation of σ=0.02 kg.a) What is the probability that any tea box will weigh less than 1 kg?b) What is the probability that any tea box will weigh higher than 1,06 kg?
- 1. The standard deviation of SAT scores is 100 points. A researcher decides to take a sample of 500 students’ scores to estimate the mean score of students in your state. What is the standard deviation of the sample mean? A) 0.2 B) 5 C) 4.47 D) 100 2. a binomial distribution with n = 10 and p = 0.2 . P(X = 5)= A) 0.34 B) 0.021 C) 0.026 D) 0.413. Calculate the mean, variance, and standard deviation of a binomial probability distribution, using the data: n = 9, x = 6, q = 0.75. a) Average b) Variance c) Standard DeviationLet X denote the data transfer time (ms) in a grid computing system (the time required for data transfer between a "worker" computer and a "master" computer. Suppose that X has a gamma distribution with mean value 37.5 ms and standard deviation 21.3. Round all answers to 4 decimal places and 3 = b) What is the probability that data transfer time exceeds 49 ms? a) What are the values of a = ? c) What is the probability that the data transfer time is between 49 and 67 ms?