Statistics: the central limit theorem 50 points!

1. when designing motorcycle helmets, the breadth of a person's head must be considered. men have head breadths that are normally distributed with a mean of 6.0 inches and a standard deviation of 1.0 inches. if one male is randomly selected, what is the probability that his head breadth is less than 6.2 inches?
a. 0.5793
b. 0.4207
c. 0.2
d. 0.8078

2. for women aged 18-24, systolic blood pressures (in mm hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1. if 4 women in that age bracket are randomly selected, find the probability that their mean systolic blood pressure is greater than 140.
a. 0.0001
b. 0.
c. 0.0274
d. 0.9726

3. a set of normally distributed data has a mean of 3.2 and a standard deviation of 0.7. find the probability of randomly selecting 30 values and getting a mean greater than 3.6.
a. 0.9991
b. 0.7157
c. 0.2843
d. 0.0009

4. a woman is randomly selected from the 18-24 age group. for woman of this group, systolic blood pressures (in mm hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1. what is the probability this woman has a systolic blood pressure greater than 140?
a. 0.9726
b. 0.0274
c. 1.92
d. 0.8665

5. the lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. what is the probability of randomly selecting a pregnant woman whose length of pregnancy is less than 260 days?
a. 0.2981
b. 0.7019
c. 0.8186
d. 0.1814

6. american women's heights are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. what is the probability of randomly selecting 150 women with a mean height greater than 64.0 inches?
a. 0.9750
b. 0.0250
c. 0.5636
d. 0.4364

7. currently, quarters have weights that are normally distributed with a mean of 5.670 g and a standard deviation of 0.062 g. a vending machine is configured to accept only those quarters with weights between 5.550 g and 5.790 g. if 280 different quarters are inserted into the vending machine, what is the probability that the mean falls between the limits of 5.550 g and 5.790 g.
a. 0.0002
b. 0.9476
c. 0.9998
d. 0.0524

8. assume that the population of human body temperatures has a mean of 98.6, as is commonly believed. also assume that the population standard deviation is 0.62. if a sample of size n=106 is randomly selected, find the probability of getting a mean temperature of 98.2 or lower.
a. 0.0001
b. 0.
c. 0.2578
d. 0.4800

9. membership in mensa requires an iq score above 131.5. nine candidates take iq tests, and their summary results indicate that their mean iq score is 133. iq scores are normally distributed with a mean of 100 and a standard deviation of 15. if one person is randomly selected from the general population, find the probability of getting someone with an iq score of at least 133.
a. 0.9861
b. 0.0139
c. 0.8810
d. 0.1190

10. a set of normally distributed data has a mean of 485 and a standard deviation of 11.6. find the probability of randomly selecting 40 values and getting a mean less than 490.
a. 0.0032
b. 0.9968
c. 0.6664
d. 0.8389