Chapter 3 Activities for the first three sections. page 1
Chapter 3, Activity 1. Continuous Uniform Distributions
In Chapter 3, we talk about the areas under the curves. Later in the text, we’ll learn to call these areas probabilities (in Ch. 10.) So, in this activity we will call these areas probabilities.
Suppose you define a continuous random variable as the time it takes to pack a customer order for shipping at a particular company and the results are uniformly distributed between 5 and 15 minutes, (i.e., the probability for each packing time is the same). The distribution is represented by the graph below.
1.
If the area of the rectangle is 1, what would be the height of the rectangle? (label the vertical axis)
2.
What is the probability that an order takes 15 minutes or less to pack?
3.
What is the probability that an order takes 12 minutes or more to pack?
4.
What is the probability that an order takes between 9 and 13 minutes to pack?
5.
What is the probability that an order takes less than 8 minutes or more than 11 minutes to pack?
6.
What is the probability that an order takes more than 25 minutes to pack?
7.
If the supervisor wants to study the 20% of orders taking the longest time to pack, he needs to study orders taking at least how long?

Chapter 3 Activities for the first three sections. page 2
a. What is the probability of randomly selecting a real number between 5 and 10? b. What is the probability of randomly selecting a real number of at least 16? c. What is the probability of randomly selecting a real number not larger than 20? ? d. At what number are 30% of the randomly selected real numbers below? e. What is the probability of randomly selecting a real number less than 0? f. What is the probability of randomly selecting a real number greater than 20 or less than 5?

Chapter 3 Activities for the first three sections. page 3
Chapter 3, Activity 2. Normal Distributions, 68-95-99.7 Rule
The Normal Curve
In a previous activity, you explored continuous uniform distributions and probabilities. Few real-life distributions are uniform. There are, however, many distributions that are approximately normal.
Exercise 1: Match the following graphs of normal distributions with the appropriate mean and standard deviation.
A B
C
3 5 7 9 11 13 15 17 19 21 23 25 27
D
3 5 7 9 11 13 15 17 19 21 23 25 27
3 5 7 9 11 13 15 17 19 21 23 25 27
2 Mean 15 and standard deviation 4
3 Mean 13 and standard deviation 2
4 Mean 15 and standard deviation 1
5 Mean 17 and standard deviation 2
3 5 7 9 11 13 15 17 19 21 23 25 27

Chapter 3 Activities for the first three sections. page 4
Exercise 2. The speed limit on a stretch of country road is 55 miles per hour (mph). A device used to measure the actual speed of cars traveling on the road finds the distribution of speeds to be approximately normal with a mean of 55 and a standard deviation of 5. Label the normal curve with the appropriate scale. Then find the probabilities using the 68-95-99.7 Rule.
      
A What is the probability that a randomly selected car on this road is traveling between
45 and 65 mph?
B What is the probability that a randomly selected car on this road is traveling between
55 and 60 mph?
C What is the probability that a randomly selected car on this road is traveling above 50 mph?
D What is the probability that a randomly selected car on this road is traveling below 45 mph?
E What is the probability that a randomly selected car on this road is traveling above 55 mph?
F What is the probability that a randomly selected car on this road is traveling between
50 and 65 mph?
Exercise 3: The average height of an adult male can be reasonably described by a normal distribution with a mean of 69 inches and a standard deviation of 2.5 inches. Find the probability of randomly selecting a male in the following categories using the Empirical Rule. For each problem, sketch a normal curve with the appropriate scale and shade the area described. Then use the 68-
95-99.7 rule to find the probability.
A What is the probability that a randomly selected male is more than 74 inches tall?
B What is the probability that a randomly selected male is between 64 and 69 inches tall?
C What is the probability that a randomly selected male is less than 61.5 inches tall?
D What is the probability that a randomly selected male is between 66.5 and 76.5 inches tall?

Chapter 3 Activities for the first three sections. page 5
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