STAT200 homework 4

Question 2Page 221, Problem 25 Text: David Lane

You are to participate in an exam for which you had no chance to study, and for that reason cannot do anything but guess for each question (all questions being of the multiple choice type, so the chance of guessing the correct answer for each question is 1/d, d being the number of options (distractors) per question; so in case of a 4-choice question, your guess chance is 0.25).

Your instructor offers you the opportunity to choose amongst the following exam formats:

i. 6 questions of the 4-choice type; you pass when 5 or more answers are correct;

II. 5 questions of the 5-choice type; you pass when 4 or more answers are correct;

III. 4 questions of the 10-choice type; you pass when 3 or more answers are correct.

Rank the three exam formats according to their attractiveness. It should be clear that the format with the highest probability to pass is the most attractive format.

a. What format provides you with the best opportunity for obtaining a passing grade?

I or II or III

b. What is your probability of passing the exam with best format?

Enter answer as a decimal rounded to 4 places without the leading 0 or as a percent rounded to 2 decimal places and no % sign.

Question 2(11 points)\

Question 2 options:

Textbook David Lane Page 269 Problem 8

http://stattrek.com/online-calculator/normal.aspx#TopPage

Assume the speed of vehicles along a stretch of I-10 has an approximately normal distribution with a mean of 71 mph and a standard deviation of 8 mph.

http://stattrek.com/online-calculator/normal.aspx

The current speed limit is 65 mph.

a. What proportion of vehicles travel less than or equal to the speed limit?

b. What proportion of the vehicles would be going less than 50 mph?

c. A new speed limit (X) will be initiated such that approximately 10% of vehicles will be over the speed limit.

What is the new speed limit (X) based on this criterion?

Question 3(11 points)

Question 3 options:

Textbook David Lane Page 270 Problem 11

http://stattrek.com/online-calculator/normal.aspx#TopPage

A group of students at a school takes a history test. The distribution is normal with a mean of 25, and a standard deviation of 4.

a. Everyone who scores in the top 30% of the distribution gets a certificate. What is the lowest score (X) someone can get and still earn a certificate?

b. The top 5% of the scores get to compete in a statewide history contest.

What is the lowest score (X) someone can get and still go onto compete with the rest of the state?

Question 4(11 points)

Textbook: Illowsky Page 361 Problem 60

The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.3 days and a standard deviation of 2.1 days.

What is the median recovery time?

Question 4 options:

	a) 2.7
	b) 5.3
	c) 7.4
	d) 2.1

Question 5(11 points)

Question 5 options:

Textbook Illowsky Page 362 Problem 66

Height and weight are two measurements used to track a child’s development. The World Health Organization measures child development by comparing the weights of children who are the same height and the same gender.

In 2009, weights for all 80 cm girls in the reference population had a mean ?= 10.2 kg and standard deviation ?= 0.8 kg.

Weights are normally distributed. X~ N(10.2, 0.8).

Calculate the z-scores that correspond to the following weights.

a. 11 kg Enter answer rounded to 2 decimal places.

b. 7.9 kg Enter answer rounded to 3 decimal places.

c. 12.2 kg Enter answer rounded to 2 decimal places.

Question 6 (11 points)

Question 6 options:

Textbook Illowsky Page 363 Problem 76

http://stattrek.com/online-calculator/normal.aspx

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet.

If X = distance in feet for a fly ball, then X ~(_____,_____) = X ~ N (250, 50)

a. If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 220 feet?

Find the probability.

b. Find the 80th percentile of the distribution of fly balls.

P(X <= x) = .80

X

Question 7 (11 points)

Textbook: Illowsky page 401 Problem 70

Which of the following ARE TRUE about the distribution for averages?

Question 7 options:

	The mean, median, and mode are equal.
	The area under the curve is one.
	The curve never touches the x-axis.
	The curve is skewed to the right.

Bottom of Form

Question 8 (11 points)

Question 8 options:

Textbook Illowsky Page 400 Problem 62

http://stattrek.com/online-calculator/normal.aspx

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. We randomly sample 49 fly balls.

If X ¯ = average distance in feet for 49 fly balls, then X ¯ ~ (_______,_______)

For the following three blank fill in the correct answer.

For blank 1

What is the appropriate distribution?

For blank 2

What is the numerical value of mean (mu) ?

For blank 3

What is the Standard deviation of the distribution?

What is the probability that the 49 balls travelled an average of less than 240 feet?

Find the 80th percentile of the distribution of the average of 49 fly balls.

Find the x value such that P(X < x) = .80

Question 9 (12 points)

Question 9 options:

Textbook Illowsky Page 406 Problem 96

A typical adult has an average IQ score of 105 with a standard deviation of 20.

If twenty (20) randomly selected adults are given an IQ test:

What is the probability that the sample mean scores will be between 85 and 125 points?

Find the probability that P (85 <= X =< 125) which is equal to P(X <= 125) - P(X <= 85)