(1) Assume that a population consists of 5 students and the marks obtained by them in a certain statistics class are 20, 15, 12, 16 and 18.

Draw all possible random samples of two students when sampling is performed

With replacement

Without replacement

Calculate the mean marks of each sample.

8. Using Figure 6.4 as a guide, sketch a normal curve for a random variable x that has a mean of 100 and a standard deviation of 10. Label the horizontal axis with values of 70, 80, 90, 100, 110, 120, and 130.

9. A random variable is normally distributed with a mean of 50 and a standard deviation of 5.

a. Sketch a normal curve for the probability density function. Label the horizontal axis with values of 35, 40, 45, 50, 55, 60, and 65. Figure 6.4 shows that the normal curve

almost touches the horizontal axis at three standard deviations below and at three standard deviations above the mean (in this case at 35 and 65).

b. What is the probability the random variable will assume a value between 45 and 55? c. What is the probability the random variable will assume a value between 40 and 60?