In this week you will learn how to calculate the mean and variance of a discrete distribution, probabilities based on binomial data and lastly probabilities based on the normal distribution.
A set of final examination marks in an introductory statistics unit is normally distributed with a mean of 73 and a standard deviation of 8.
a. What is the probability of getting a mark of 91 or less?
b. What is the probability that a student obtains a mark between 65 and 89?
c. If the lecturer gives Distinction and High Distinction grades to the top 15% of students, what mark does a student need to get a distinction?
d. If the lecturer gives grades of High Distinction to the top 5% of students, are you better off with a mark of 80 on this exam or a mark of 68 on a different exam where the mean is 62 and the standard deviation is 3? Show your answer statistically and explain.
Suppose the height of college basketball players follows a normal distribution with mean height 76 inches, and standard deviation inches.
a. What are the Z scores for a height of 78 inches and 74 inches respectively?
b. Use empirical rules to decide the proportion of players whose height fall between 74 and 78 inches. Or Use empirical rule to decide the probability of a randomly selected player whose height falls between 74 and 78 inches.
c. Nearly 95% of players whose height fall between what two values? Use empirical rules.