Question

MAIN QUESTION: In last week’s graded homework (week 3) you were given the mean and standard deviation for weight of the entire data set. If we assume weights are normally distributed, what is the probability that the weight of a sample of 10 people would be more extreme (farther away from the mean) than the average weight from your personal sample of 10 people (you will need to calculate this using your personal sample from week 1). Use the results to state whether your particular sample of 10 was usual or unusual. Explain.

MEAN: 165.1

STANDARD DEVIATION: 36.3

My Personal Sample of 10:

1. 235

2. 206

3. 182

4. 140

5. 158

6. 215

7. 171

8. 275

9. 151

10. 130

Answer 1

I assume that the Mean and the SD given are the population mean and SD, The given data of the weight of the 10 students' average is

	Weight
	235
	206
	182
	140
	158
	215
	171
	275
	151
	130
Mean	186.3

We know that the sampling distribution of teh mean is Normal with mean and sd .

Therefore for the mean weight of 186.3, the Z is

  

  

  

The Z-value corresponding to the avaerage weight is 1.8468. By the empirical rule, this value is within the 2 limits and hence the given sample of 10 is a usual one.