If the quality of individual boards varies according to a normal distribution with mean µ = 100 and standard deviation σ = 4 , what will be the distribution of the sample averages? (Recall the sample size is n = 5.)

The distribution of sample averages will have a normal distribution withe mean = 100 and a stamdard deviation of 1.789.

Step-by-step explanation:

According to the central limit theorem, the mean of the distribution of sample means is equal to the population mean.

μₓ = μ = 100

The theorem goes further to explain that if samples of finite size are obtained from the population, the distribution of sample means will approximate the distribution of the population. Since the population is known to have data that is distributed normally, the distribution of sample means will have a normal distribution too.

The standard deviation of the distribution of sample means is given as the standard error of the mean,

σₓ = (σ/√n)

where σ = population standard deviation = 4

n = sample size = 5

σₓ = (4/√5) = 1.789

Hope this Helps!!!

The answer is, with a  mean 100 and a standard deviation of 4/ root 5.

Step-by-step explanation:

From the given question, let us recall the following,

Normal distribution with µ = 100

The standard deviation σ =4

the sample size n =5

Therefore,

The distribution of x will be normal with the mean 100 and a standard deviation of 4/ root 5,  

Which is denoted as,

Mean 100 = 4√5

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step-by-step explanation:

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6. 104

7. 52/37

8. 2704

9. 140608

10. -52

11. |52|=52

12. 1/52

13. 156

14. 26

15. 40

16. 37

17. -364

18. 53 1/3

19. 50.96

20. 43 2/3

21. 78

22. 50.75

23. 47.63

24. 163.28

25. 10400

26. 338

27. 208

28. 2704 square inches

29. 312 square meters

30. don't know what its asking, tell me so i can tell you

31. 8490.56

32. 52 degrees would be an acute angle

33. 128 degrees

34. 20.8

35. 39

36. 208