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Mean of sampling distribution of sample

A supermarket receives a shipment of 20,000 cans of beans. The supermarket picks a random sample 100 cans and finds their weights. If the mean of the weights of the cans in the shipment is known to equal 20, and the standard deviation of the weights of the cans in the shipment is known to equal 5, then

a. What is the mean of sampling distribution of sample mean X(X- bar) ?

b. What is the variance of sampling distribution of sample mean X(X-bar) ?

c. For a sample with size 100, what is the probability that the sample mean exceed 20?

d. For a sample with size 100, what is the probability that the sample mean exceed 19?

e. For a sample with size 100, what is the probability that the sample mean is less than 21?

f. For a sample with size 100, what is the probability that the sample mean lies between 20 and 21?

g. For a sample with size 100, what is the probability that the sample mean lies between 19 and 21?

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## Q : Hypothetical joint probability density function

The consumption of two types of manufacturing goods (X and Y) follows a hypothetical joint probability density function as follows: