Intro to Statistics

1. 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?

Enter N for Normal Dstribution (parent)

Enter Ns for Normal Sampling Distribution

Enter t for Student t distribution

For blank 2  What is the numerical value of mean( mu) ?

Enter answer with 2 decimal precision.

For blank 3  What is the Standard deviation of the distribution?

Enter answer with 2 decimal place precision.

b. What is the probability that the 49 balls traveled an average of less than 240 feet? 

The P(Xbar < 240)

Enter answer to 3 decimal place precision.

Do not enter answer as a percent

Do not include a 0 to the left of the decimal point. 

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

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

Enter answer to 1 decimal place precision.  Do not include the 0 to the right of the decimal point.

2.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.

3.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.

The current speed limit is 65 mph.

a.    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?

P(x<= X) = .90

Enter answer rounded to 1 decimal place. 

4. 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 obtaing 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.