1. Determine the following probability for the standard normal distribution.

a)P(z < 2.4)

b)P(-1.5 z 2.2 )

c)P(0.6 z 2.3)

d)P(z> 1.8)

2. Suppose that a normal random variable has mean = 10 and standard deviation of s=2. Find the probabilities of the following x values.

a) x < 12.1 b)x > 9.2 c) 8.4 < x < 10.3

3. A radar unit is used to measure speeds of cars on a highway. The speeds are normally distributed with a mean of 90 km/hr and a standard deviation of 10 km/hr. What is the probability that a car picked at random is travelling at more than 100 km/hr?

4. A local bank issues Visa Card credit cards. The balances on all credit cards issued by the bank is estimated that have a mean of RM845 and a standard deviation of RM270. Assume that the balances on all these visa cards follow a normal distribution.

(a) What is the probability that a randomly selected Visa card issued by this bank has a balance between RM1000 and RM1400?

(b) What percentage of the Visa cards issued by this bank has a balance of RM750 or more?

5. A normal variable x has an unknown mean and standard deviation s= 2. If the probability that x exceeds 7.5 is 0.8023, find .

6. A national test is required before applying for a place in a university. The scores on this test are normally distributed with a mean of 500 and a standard deviation of 100. Ashraf wants to be admitted to this university and he knows that he must score better than at least 70% of the students who took the test. He takes the test and scores 585. Will he be admitted to this university?

7. A large group of students took a test in Social Statistic 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)?