5 In a manufacturing process a machine produces bolts that h

5. In a manufacturing process a machine produces bolts that have an average length of 3 inches with a variance of .03. If we randomly select three bolts from this process: What is the probability the mean length of the bolt is less than 3.16 inches?
A. 5.48%
B. 97.72%
C. 94.52%
D. 44.52%
E. 2.28%

6. In a manufacturing process a machine produces bolts that have an average length of 3 inches with a variance of .03. If we randomly select three bolts from this process: What is the probability the mean length of the bolt is at least 3.1 inches?
A. 84.13%
B. 100%
C. 71.57%
D. 28.43%
E. 15.87%

7. The width of a confidence interval will be:
A. Narrower for 99% confidence than 95% confidence
B. Narrower for a sample size of 100 than for a sample size of 50
C. Wider for 90% confidence than 95% confidence
D. Wider when the sample standard deviation (s) is small than when s is large

8. A confidence interval increases in width as
A. the level of confidence decreases
B. sample size n increases
C. s decreases
D. all of the above
E. none of the above

5. Here it is given that the mean length of the bolt produced by a manufacturing process is 3 inches with variance 0.03 inches.

Let us assume that the length of bolts follow normal distribution with 3 inches and variance 0.03 inches or standard deviation 0.1732 inches.

Then the probability that the length of bolt is 3.16 inches refers to P (X < 3.16) and can be obtained using Excel function NORMDIST (x, mean, standard deviation, 1).

Therefore, enter the formula = NORMDIST ( 3.16, 3, 0.03, 1 ) and get the probability as 0.8222.

Hence 82.22% bolts will have the length less than 3.16 inches.

6. Here it is given that the mean length of the bolt produced by a manufacturing process is 3 inches with variance 0.03 inches.

Let us assume that the length of bolts follow normal distribution with 3 inches and variance 0.03 inches or standard deviation 0.1732 inches.

Then the probability that the length of bolt is at least 3.1 inches refers to P (X > 3.1) = P( X< 3.1) and can be obtained using Excel function NORMDIST (x, mean, standard deviation, 1).

Therefore, enter the formula = NORMDIST ( 3.1, 3, 0.03, 1 ) and get the probability as 0.7181 and then subtract it from 1 to get the required probability as 0.2819.

Hence 28.19% bolts will have the length of at least 3.16 inches.

7. The width of a confidence interval will be:

D. When the sample standard deviation (s) is smaller than when the standard deviation (s) is large.

8. A confidence interval increases in width as

- level of confidence increases

- Samaple size decreases

- S ( standard deviation) decreases

That is , D. All of the above