Answer the following. Include the solutions. Include also the diagrams and shade the required area.

1. Find the z-score corresponding to the given area of the normal curve with the following given values:

a. area to the left of z is .8461

b. area to the left of -z is .2514

c. area to the right of z is .4207

d. area to the right of -z is .6736

e. area to the left of z is .7518

2. Find the area of the normal curve given the following:

a. from z=0 to z=1.43

b. from z= -1.23 to z=0

c. from z=2.38 to z=3.09

d. from z=-1.42 to z=2.37

e. from z=-2.35 to z=2.48

3. An entrance examination is to be conducted to 1500 incoming freshmen students at Gordon College which is known to be normally distributed and has a mean of 85 and a standard deviation of 10.

a. How many students would be expected to score above 95?

b. How many students would be expected to score between 75 and 115?

4. A nurse commutes daily from his urban home to his midtown hospital. On the average trip one way takes 24 minutes, with a standard deviation of 3.8 minutes. Assume the distribution of trips times to be normally distributed.

a. What is the probability that a trip will take at least hour?

b. If the time of his duty is 9:00 am and he leaves his house at 8:45 am daily, what percentage of the time is he late for work?

c. If he leaves the house at 8:35 am and coffee is served at the hospital from 8:50am until 9:00am, what is the probability that he misses coffee?

5. The weight of newborn babies in James Gordon Memorial Hospital is normally distributed with a mean of 6.9 pounds and a standard deviation of 1.2 pounds.

a. How unusual is a baby weighing 8.0 pounds or more?

b. What would be the 90th percentile for birth weight?

c. Within what range would the middle 95 percent of births weights lie?

6. A large group of students took a test in Statistics and the final grades have a mean of 70 and a standard deviation of 10. If we can approximate the distribution of these grades by a normal distribution, what percent of the students;

a. scored higher than 80?

b. should pass the test (grades60)?

c. should fail the test (grades<60)?

7. The lengths of similar components produced by a company are approximated by a normal distribution model with a mean of 5 cm and a standard deviation of 0.02 cm. If a component is chosen at random.

a. What is the probability that the length of this component is between 4.98 and 5.02 cm?

b. What is the probability that the length of this component is between 4.96 and 5.04 cm?

8. The annual salaries of employees in a large company are approximately normally distributed with a mean of P50,000 and a standard deviation of P20,000.

a. What percent of people earn less than P40,000?

b. What percent of people earn between P45,000 and P65,000?

c. What percent of people earn more than P70,000?

9. All freshmen students took a test in Statistics and the final grades have a mean of 80 and a standard deviation of 20. If we can approximate the distribution of these grades by a normal distribution, what percent of the students;

a. scored higher than 90?

b. pass the test (grades 70)?

c. fail the test (grades < 70)?

10. The annual salaries of employees in a large company are approximately normally distributed with a mean of P 60,000 and a standard deviation of P30,000.

a. What percent of people earn less than P50,000?

b. What percent of people earn between P55,000 and P75,000?

c. What percent of people earn more than P80,000?