You completed problems 1-3 by means of approximation. Now that you know how to convert into z scores, find the exact values and compare them to the values you got in section 6.1

1. The fictitious weights (in lbs.) of your patients are normally distributed with a mean of 202 lbs. and a standard deviation of 17 lbs.

a. If one patient is picked randomly, find the probability that their weight is above 195lb.

b. Find a weight x30 so that the weight of any 70% of random patients is above x.

2. If the average salary of Nurses in New York States is normally distributed with the mean of $81,675 and standard deviation of $5,400, find the probability for a randomly selected nurse to earn:

a. More than $81,000.

b. Between $70,000 and $85,000.

c. What is the probability that the mean salary of a random sample of 4 nurses is more than $85,000?

3. An environmental group did a study of recycling habits in a California community. It found that 70 percent of aluminum cans sold in the area were recycled. If 400 cans are sold in one day, what is the probability that between 260 and 300 will be recycled?

4. Use Table 5 of Appendix II to find the area between z = 1.00 and z = 2.70.

Let x be a normally distributed random variable representing the scores of Prof. Fernndez's exam 1 over his last three MAT 134 courses with = 85 and standard deviation = 14. For each of the following probabilities, draw an appropriate diagram, shade the appropriate region and then determine the value:

a. ( > 76)

b. (x < 58)

c. (P(61.2 < x < 85.2)

d. (70 < x < 80.4)