1. Suppose zz is the standard normal variable. Draw the normal curve for each of the following probability statements to visualize the required area. Report answers accurate to at least 4 decimal places.

1. P(z1.63)=
2. P(z>0.93)=
3. P(z<0)=
4. P(z>5.82)=
5. P(-1.43z<2.43)=
6. P(-2.25
7. P(z<-1.17 given z<0)=
8. P(z0.67orz>2.43)=
9. P(z<1.87orz1.63)=
10. P(z=0.67)=

3. Given zz is the standard normal random variable, find c>0c>0 such that P(c

4. The annual rainfall in a certain region is approximately normally distributed with mean 40.2 inches and standard deviation 5.2 inches. Round answers to the nearest tenth of a percent. a) What percentage of years will have an annual rainfall of less than 43 inches? % b) What percentage of years will have an annual rainfall of more than 38 inches? % c) What percentage of years will have an annual rainfall of between 37 inches and 42 inches? %

5. A particular fruit's weights are normally distributed, with a mean of 553 grams and a standard deviation of 27 grams. If you pick one fruit at random, what is the probability that it will weigh between 495 grams and 533 grams?

6. A particular fruit's weights are normally distributed, with a mean of 683 grams and a standard deviation of 16 grams. The heaviest 17% of fruits weigh more than how many grams? Give your answer to the nearest gram.