Problem 1

A nurse measured the blood pressure of each person who visited her clinic. Following is a relative-frequency histogram for the systolic blood pressure readings for those people aged between 25 and 40. Use the histogram to answer the question. The blood pressure readings were given to the nearest whole number.

(a)

Approximately what percentage of the people aged 25-40 had a systolic blood pressure reading less than 120 mm Hg?

• [ ] A) 15%
• [ ] B) 75%
• [x] C) 50%
• [ ] D) 35%
• [ ] E) 25%

(b)

Given that 200 people were aged between 25 and 40, approximately how many had a systolic blood pressure reading less than 130?

• [ ] A) 70
• [ ] B) 25
• [ ] C) 100
• [ ] D) 50
• [x] E) 150

(c)

Which of the following is true for systolic Blood Pressure

• [ ] A) Mean and Median are same because the histogram is symmetric
• [ ] B) Mean is greater than median because histogram is left-skewed
• [x] C) Mean is greater than median because histogram is right-skewed
• [ ] D) Median is greater than mean because histogram is left-skewed
• [ ] E) Median is greater than mean because histogram is right-skewed

Problem 2

The exam scores for all students taking an introductory Statistics course are used to construct the following box plot.

(a)

Based on this box plot, the interquartile range is closest to

• [ ] A) 10
• [x] B) 25
• [ ] C) 50
• [ ] D) 80
• [ ] E) 75

(b)

If 5 points were added to each score, then

• [ ] A) the third quartile would increase by 5 points.
• [ ] B) the median score would increase by 5 points.
• [ ] C) the interquartile range would remain unchanged.
• [ ] D) Only A) and B) are correct
• [x] E) A), B) and C) all are correct.

(c)

If 5 points were added to each score, then standard deviation of the new scores would

• [ ] A) be increased by 5.
• [ ] B) be increased by 25.
• [x] C) remain unchanged.
• [ ] D) be decreased by 5.
• [ ] E) be decreased by 25.

Problem 3

If the sample space is and if and

(a)

Find

(b)

Are and independent? Why or why not?

and are independent iff the following condition is true

Because the condition is not true and are not independent

Problem 4

Draw a Venn Diagram involving sets , , and where and are mutually exclusive, and are disjoint and .

Problem 5

Let denote the distance (m) that an animal moves from its birth site to the first territorial vacancy it encounters. Suppose that banner-tailed kangaroo rats, has an exponential distribution with parameter .

(a)

What is the probability that the distance is between 100m and 220m

(b)

What is the value of the median distance?

(c)

In language that is clear and accurate, provide an interpretation of the probability expression

When a kangaroo rat travels over 100m from it's birthplace the probability that it'll travel less than 50m farther is 0.478.

Problem 6

Suppose that . Using a standard normal table, calculate .

Problem 7

Suppose and are two independent random variables, where and . Let . Showing all the required steps, find the pdf of .