# Sampling distibutions, central limit theorem, probability

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4. A computer supply house receives a large shipment of floppy disks each week. Past experience has shown that the number of flaws per disk can be described by the following probability distribution:

Number of Flaws per Floppy Disk Probability

0 .65

1 .2

2 .1

3 .05

a. Calculate the mean and standard deviation of the number of flaws per floppy disk.

b. Suppose that we randomly select a sample of 100 floppy disks. Describe the shape of the sampling distribution of the sample mean X. Then compute the mean and the standard deviation of the sampling distribution of X.

c. Sketch the sampling distribution of the sample mean X and compare it to the distribution describing the number of flaws on a single floppy disk.

d. The supply house's managers are worried that the floppy disks being received have an excessive number of flaws. Because of this, a random sample of 100 disks is drawn from each shipment and the shipment is rejected (sent back to the supplier) if the average number of flaws per disk for the 100 sample disks is greater than .75. Suppose that the mean number of flaws per disk for this week's entire shipment is actually .55. What is the probability that this shipment will be rejected and sent back to the supplier?

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This solution concerns sampling distributions, the central limit theorem, and calculating probability from a sampling distribution.

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Sampling Distributions

4. A computer supply house receives a large shipment of floppy disks each week. Past experience has shown that the number of flaws per disk can be described by the following probability distribution:

Number of Flaws per Floppy Disk Probability

0 .65

1 .2

2 .1

3 .05

a. Calculate the mean and standard deviation of the number of flaws per floppy disk.

Create a table with five columns as follows:

1. The first column lists the values of the random variable .

2. The second column lists the probability for each value of.

3. Multiply the values in the first and second column to get , the values in the third column.

4. Square the values of to get the values of in the fourth column.

5. Multiply the values of and to get the values in the fifth column.

For this probability distribution, the table is:

The mean of ...

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