Question

x | p(x)

----------

6 0.236

7 0.063

8 0.214

9 0.262

10 0.225

Suppose that samples of 100 are generated from the probability distribution and the mean of each sample is recorded.

1. Find the mean of the sample means.

2. find the standard deciation of the sample means.

3. The weights of quarters are normally distributed with a mean of 5.64 and a standard deviation of 0.218 grams. Every item in a vending machine is $1.

suppose that the vendors consider a rejection rate of more than 2% to be unacceptable. This means that they only want to reject 1% of quarters for being too heavy and 1% of quarters for being too light. Compute the upper and lower limits for acceptable weights that the vending machine should be programmed to accept. (Round your answers to 2 decimal places, show work.)

Answer 1

1.

x	p(x)	x*p(x)
6	0.236	1.416
7	0.063	0.441
8	0.214	1.712
9	0.262	2.358
10	0.225	2.25
Sum	1	8.177
	Mean	8.177

2.

x	p(x)	x*p(x)	x²*p(x)
6	0.236	1.416	8.496
7	0.063	0.441	3.087
8	0.214	1.712	13.696
9	0.262	2.358	21.222
10	0.225	2.25	22.5
Sum	1	8.177	69.001
	Mean	8.177
	Variance	2.137671
	Standard deviation	1.462078

3. z = -2.33 and 2.33

Lower limit = -2.33*0.218 + 5.64 = 5.13

Upper limit = 2.33*0.218 + 5.64 = 6.15

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