14:38. The income distribution of officers of a certain company was found to follow normal distribuiton. The average income of an officer was Rs. 15,000.00. The standard deviation of the income of officers was Rs. 5,000.00. If there were 242 officers drawing salary above Rs. 18,500.00, how many officers were there in the company ?

9. The number of births per woman in China is 1.6 down from 5.91 in 1966. This fertility rate has been attributed to the law passed in 1979 restricting births to one per woman. Suppose that a group of students studied whether or not the standard deviation of births per woman was greater than 0.75. They asked 50 women across China the number of births they had had. The results are shown in the following table. Does the students’ survey indicate that the standard deviation is greater than 0.75? Use α = 0.01. # of Births Frequency         0                5         1               30         2               10         3                5

2. A statistic test has a mean of 78 and a standard deviation of 6. a) What is the z-score of a student who scored 89 on the test? b) What is the z-score of a student who scored 64 on the test? c) What is the z-score of a student who scored 78 on the test? d) What is the score of a student whose z-score is 1.24? e) What is the score of a student whose z-score is -.31? f) What is the score of a student whose z-score is -1? 3. For males in a certain towWn, the systolic blood pressure is normally distributed with a mean of 135 and a standard deviation of 8. a) What is the probability that a randomly selected male's systolic blood pressure will be greater than 143? b) What is the probability that a randomly selected male's systolic blood pressure will be less than 119?

For the statistics test scores the mean is 63 and the standard deviation is 7.0 and for the biology test scores the mean is 23 and the standard deviation is 3.9. a) A student who took both tests scored a 69 on the statistics test and a 26 on the biology test. Transform each test score to a standard z-score and determine on which test the student had a better score. b) If a student who took both tests has a standard z-score of a -1.67 on the statistics test and a 2.05 on the biology test, find the students actual test scores.