Statistical concepts/ Deviation

Question 1. Find the standardized variable z if x has Mean 12 and standard deviation 10. Z = (x-10)/12
Z = (x-12)/10
Z = (12-x)/10
Z = (x+12)/10

Question 2. Find the area under the standard normal curve to the right of z = 1.55. Round to four decimal places.
.9394
.9505
.0606
.0485

Question 3. Find the area under the standard normal curve to the left of z = 2.33
.0099
.0102
.9901
.4901

Question 4. Find the area under the standard normal curve over the interval z = -0.44 to z = 0.44. Compute probabilities using the standard normal table in Appendix B (Table 3). Round the answer to four decimal places.
0.3300
0.3400
0.3500
0.3600

Question 5. Scores on a certain nationwide college entrance examination follow a normal distribution with a mean of 550 and a standard deviation of 100. Find the probability that a student will score over 680. Round your answer to four decimal places.
0.1587
0.0968
0.1459
0.9032

Question 6. Scores on a certain nationwide college entrance examination follow a normal distribution with a mean of 600 and a standard deviation of 100. Find the probability that a student will score between 410 and 700. Round your answer to four decimal places.
0.9635
0.7826
0.8347
0.8126

Question 7. A population has mean 70 and standard deviation 15. Calculate mean of x bar for a random sample of size 20.
15
3.5
.75
70

Question 8. A population has mean 37 and standard deviation 6. Calculate the standard deviation of x bar for a random sample of size 29.
1.1
1.3
.8
1.6

Question 9. Suppose the weights of packages of lettuce coming off a packaging line have a normal distribution with mean 8.4 ounces and standard deviation 0.4 ounce. If every package is labeled 9.2 ounces, what proportion of the packages weigh less than the labeled amount?
76%
84%
98%
87%

Question 10. Suppose the weights of the contents of cans of mixed nuts have a normal distribution with mean 32.4 ounces and standard deviation 0.4 ounce.

If two packages are randomly selected, what is the probability that the average weight is less than 32 ounces?
1.7%
7.9%
7.1%
2.5%