The following are the ages of a group of tourists visiting The Library of Congress:

1.      The following are the ages of a group of tourists visiting The Library of Congress:

36, 38, 33, 44, 37, 37, 38, 34, 34, 36, 34, 40, 42, 41, 35, 48, 31, 33, 46, 47, 33, 36, 37, 37, 34, 39, 35, 37, 36, 39, 39

a)      Construct the Histogram of the ages with a class width of 5 years.

b)     Find the mean of the dataset.

c)      Find the median of the dataset.

 2. True or false - for the dataset: 13, 13, 15, 15, 16, 16, 16, 17, 18, 22

a)      The maximum value of the dataset above is 22. If the analyst makes one mistake and record it as 2.2, then the mistake will change the mean and the median of the dataset. Show calculations.

b)     If the variance of a dataset is zero, then all observations must also be zero.

c)      The standard deviation of dataset cannot be negative.

d)     The variance of a dataset is always positive.

e)     The following graph have a negative correlation:

3.      A shipment of thirteen smartphones contains three with cracked screens. If sold in a random order, what is the probability that the first ten sold have undamaged screen?

4.      When you toss a fair six-faced die two times many outcomes can happen:

a)      Determine the number of possible outcomes in the sample space. Explain your answer.

b)     Calculate the probability that you get a number greater than 5 at the first toss. Show work and write the answer in the simplest fraction form.

c)      Calculate the probability that the sum of the two tosses is at lest 7. Show work and write the answer in the simplest fraction form.

d)     Calculate the probability that the sum of the two tosses is at least 7, given that you get a number greater than 2 in the first toss. Show work and write the answer in the simplest fraction form.

e)     If event A is "Getting a number greater than 4 in the first toss", and event B is "The sum of two tosses is at least 8". Are event A and event B independent. Justify your answer.

5.      The SAT Math scores for all seniors in a High Schools are normally distributed with population standard deviation of 200. If 100 seniors from the school are randomly selected, and their SAT Math scores have a sample mean of 650, determine:

1.      What distribution will you use to determine the critical value for a confidence interval estimate of the mean SAT Math score for the seniors in the High School? Why?

2.      Construct a 95% confidence interval estimate of the mean Math score for the seniors in the High School. Show work and round the answer to two decimal places.

6.      There are sixteen shirts in your closet, eight blue and eight green. You randomly select one shirt to wear on Monday, and then a different one on Tuesday. You wear a blue shirt on Monday and a green shirt on Tuesday. Determine whether the scenario involves independent or dependent event. Find the probability.

7.      You are setting the combination on a four-digit lock. You want the number 1234 but don´t care what order they are in. Find the number of possibilities.

8.      Is a 90% confidence interval estimate of the mean SAT Math score wider than the 95% confidence interval estimate you got from part 2 in Problem 5