Let A be a random variable corresponding to the sum of the outcomes of two independent rolls of a fair 6-sided die (numbered from 1 to 6). Determine the variance of A.
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Let A be a random variable corresponding to the sum of the outcomes of two independent rolls of a fair 6-sided die (numbered from 1 to 6). Determine the variance of A.
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- Compute the variances of the two random variables whose probability tables are given in Table 7. Relate the sizes of the variances to the spread of the values of the random variables. Table 7 Outcome Probability 2 .1 4 .4 (a) 6. .4 .1 2 .3 4 .2 (b) .2 8 .3The Australian sheep dog is a breed renowned for its intelligence and work ethic. It is estimated that 30% of adult Australian sheep dogs weigh 65 pounds (lbs) or more. A sample of 40 adult dogs is studied and follows a binomial distribution. Let X be a binomial random variable that represents the number of adult dogs in the sample who weigh 65 lb or more. a. Find the mean number of dogs in this sample who weigh 65 lb or more. Mean = b. Find the standard deviation of the number of dogs in the sample who weigh 65 lb or more. Round to three places. Standard deviation =Rods are produced in large quantities in a factory. The masses of these rods are normally distributed with mean 250g and variance 9g. A random sample of 100 rods is selected. Find the probability that the mean mass of the rods in the sample will lie between 249g and 251g. If the rods are produced in batches of n and a batch is selected at random, find the least value of n such that the probability that the mean mass of the rods in the batch will lie between 249g and 251g is greater than 0.95.
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- The 5 crew members of the exploration team of the spaceship Enterprise under the command of Captain Kirk are 162, 172, 177, 180 and 184 cm in height, respectively. Calculate the expected value and variance of the height of a randomly selected person among these 5 crew members. ( explaining them to someone who does not know anything about the subject)A survey of prison guards shows that their average starting hourly wage is $30 and the variance is 9. If prison guard is selected, what is the probability that his/her hourly wage will be greater than $27 but less than $35?