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Stats & Probabaility Multiple Problems Step-by-Step Solution

Question # 00012784
Subject: Statistics
Due on: 05/12/2014
Posted On: 04/19/2014 08:29 AM

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Refer to the following frequency distribution for Questions 1, 2, 3, and 4. Show all work. Just the answer, without supporting work, will receive no credit.

The frequency distribution below shows the distribution for checkout time (in minutes) in
UMUC MiniMart between 3:00 and 4:00 PM on a Friday afternoon.
Checkout Time (in minutes) Frequency
1.0 -­? 1.9 5
2.0 -­? 2.9 6
3.0 -­? 3.9 4
4.0 -­? 4.9 3
5.0 -­? 5.9 2
1. What percentage of the checkout times was less than 3 minutes? (5 pts)
2. Calculate the mean of this frequency distribution. (5 pts)
3. Calculate the standard deviation of this frequency distribution. (10 pts)
4. Assume that the smallest observation in this dataset is 1.2 minutes. Suppose this observation were incorrectly recorded as 0.12 instead of 1.2. Will the mean increase, decrease, or remain the same? Will the median increase, decrease or remain the same? Explain your answers. (5 pts)

Refer to the following information for Questions 5 and 6. Show all work. Just the answer, without supporting work, will receive no credit.

A 6-faced die is rolled two times. Let A be the event that the outcome of the first roll is greater than
4. Let B be the event that the outcome of second roll is an odd number.

5. What is the probability that the outcome of the second roll is an odd number, given that the first roll is greater than 4? (10 pts)
6. Are A and B independent? Why or why not? (5 pts)


Refer to the following data to answer questions 7 and 8. Show all work. Just the answer, without supporting work, will receive no credit.

A random sample of STAT200 weekly study times in hours is as follows:

4 14 15 17 20

7. Find the standard deviation. (10 pts)
8. Are any of these study times considered unusual in the sense of our textbook? Explain.
Does this differ with your intuition? Explain. (5 pts)

Refer to the following table for Questions 9, 10, and 11. Show all work. Just the answer, without supporting work, will receive no credit.

The table shows temperatures on the first 12 days of October in a small town in Maryland.

Date Temperature Date Temperature Date Temperature
Oct 1 73 Oct 5 53 Oct 9 66
Oct 2 66 Oct 6 52 Oct 10 49
Oct 3 65 Oct 7 62 Oct 11 53
Oct 4 70 Oct 8 55 Oct 12 57

9. Determine the five-number summary for this data. (10 pts)
10. Determine the mean temperature. (3 pts)
11. Determine the mode(s), if any. (2 pts)
Refer to the following information for Questions 12 and 13. Show all work. Just the answer, without supporting work, will receive no credit.

There are 1000 students in the senior class at a certain high school. The high school offers two Advanced Placement math / stat classes to seniors only: AP Calculus and AP Statistics. The roster of the Calculus class shows 100 people; the roster of the Statistics class shows 80 people. There are 45 overachieving seniors on both rosters.

12. What is the probability that a randomly selected senior is in at least one of the two classes
? (10 pts)
13. What is the probability that a randomly selected senior takes only one class? (10 pts)

Refer to the following information for Questions 14, and 15. Show all work. Just the answer, without supporting work, will receive no credit.

A box contains 10 chips. The chips are numbered 1 through 10. Otherwise, the chips are identical. From this box, we draw one chip at random, and record its value. We then put the chip back in the box. We repeat this process two more times, making three draws in all from this box.

14. How many elements are in the sample space of this experiment? (5 pts)
15. What is the probability that the three numbers drawn are all multiples of 3? (10 pts)

Questions 16 and 17 involve the random variable x with probability distribution given below.
Show all work. Just the answer, without supporting work, will receive no credit.

x 2 3 4 5 6
P( x) 0.1 0.2 0.3 0.1 0.3

16. Determine the expected value of x. (10 pts)
17. Determine the standard deviation of x. (10 pts)
Consider the following situation for Questions 18, 19 and 20. Show all work. Just the answer, without supporting work, will receive no credit.

Mimi just started her tennis class three weeks ago. On average, she is able to return 15% of her opponent’s serves. Let random number X be the number of serves Mimi returns. As we know, the distribution of X is a binomial probability distribution. If her opponent serves 10 times, please answer the following questions:
18. What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively?

19. Find the probability that she returns at least 2 of the 10 serves from her opponent .

20. Find the mean and standard deviation for the probability distribution.
Refer to the following information for Questions 21, 22, and 23. Show all work.
The heights of pecan trees are normally distributed with a mean of 10 feet and a standard deviation of 2 feet.
21. What is the probability that a randomly selected pecan is between 10 and 12 feet tall?

22. Find the 90th percentile of the pecan tree height distribution.

23. If a random sample of 25 pecan trees is selected, what is the standard deviation of the sample mean?

24. A random sample of 225 SAT scores has a mean of 1500. Assume that SAT scores have a population standard deviation of 300. Construct a 95% confidence interval estimate of the mean SAT scores. Show all work.

27. A certain researcher thinks that the proportion of women who say that the earth is getting warmer is greater than the proportion of men. The research conducted a survey, and found the following result :

In a random sample of 250 women, 70% said that the earth is getting warmer.

In a random sample of 200 men, 67% said that the earth is getting warmer.
Assume we want to use a 0.05 significance level to test the claim.

(a) Identify the null hypothesis and the alternative hypothesis.

(b) Determine the test statistic. Show all work

(c) Determine the critical value. Show all work

(d) Is there sufficient evidence to support the claim that the proportion of women saying the earth is getting warmer is higher than the proportion of men saying the earth is getting warmer? Justify your conclusion. (25 pts)

Refer to the following data for Questions 28 and 29. :

x 0 -1 1 2 3

y 3 -2 5 6 8
28. Find an equation of the least squares regression line. Show all work

29. Based on the equation from # XXXXX what is the predicted value of y if x = 4?


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Stats & Probabaility Multiple Problems Step-by-Step Solution

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Posted On: 04/19/2014 08:31 AM
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Tutorial Preview …+ x = xx The total xxxxxx of checkout xxxxx is x x 6 x 4 + x + 2 x 20 xxx xxxxxxxxxx is xxxxxxxxxxxx = 55%2 xxxxxxxxx the mean xx this xxxxxxxxx xxxxxxxxxxxx The xxxx is calculated xxxxxxxxxx xm is xxx midpoint xx xxxx class, xxx fi is xxx corresponding frequency xxxxxxx class x xxxxxxxxx the xxxxxxxx deviation of xxxx frequency distribution xxxxxxxxxxxxx (x)Frequency xxxx x x x x-barf*d*d1 0 x 1 91 xxxxx 5512 xxxxx x - x 92 456-0 xxx 8153 0 x 3 xx xxxx 450 xxx 0…
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Stats_Probabaility_Multiple_Problems_Solution.docx (835.46 KB)
Preview: will xxx affect xxx median value xxx value that xxx in xxx xxxxxx of xxx data set xxxx not change xxxxx to xxx xxxxxxxxx information xxx Questions 5 xxx 6 Show xxx work xxxx xxx answer, xxxxxxx supporting work, xxxx receive no xxxxxx A xxxxxxx xxx is xxxxxx two times xxx A be xxx event xxxx xxx outcome xx the first xxxx is greater xxxx 4 xxx x be xxx event that xxx outcome of xxxxxx roll xx xx odd xxxxxx 5 What xx the probability xxxx the xxxxxxx xx the xxxxxx roll is xx odd number, xxxxx that xxx xxxxx roll xx greater than xx (10 pts)Event x is xxxxxxxx xxxx is xxxxxxx than 4” xxxxx B is xxxxxxxxx roll xx xx odd xxxxxxxxx To determine xxx and B), xxxxxxxx that xxxxx xxx only x ways to xxxx a value xxxxxxx than xx xxx then xxxxx are 3 xxxx to roll xx odd xxxxxx xxx total xxxxxx of ways xxxx you can xxxx a xxxxx xxxxxxx than x followed by xx odd number xx 2*3 x x Since xxxxx are 36 xxxxxxxx combinations of xxxxxx for xxx xxx rolls, xxx probability of xxxxxxx a value xxxxxxx than x xxxxxxxx by xx odd number xx 6/36, or xxx 6 xxx x and x independent? Why xx why not? xx pts)If x xxx B xxx independent, then xxx and B) x P(A)P(B) xxxx xx above, xxx and B) x 1/6, and xxxx = xxx xxxxx Since xxx and B) x P(A)P(B), the xxx events xxx xxxxxxxxxxx Refer xx the following xxxx to answer xxxxxxxxx 7 xxx x Show xxx work Just xxx answer, withoutsupporting xxxxx will xxxxxxx xx credit x random sample xx STAT200 weekly xxxxx times xx xxxxx is xx follows: 4 xx 15 17 xxx Find xxx xxxxxxxx deviation xxx pts) 8 xxx any of xxxxx study xxxxx xxxxxxxxxx unusual xx the sense xx our textbook? xxxxxxx ?Does xxxx xxxxxx with xxxx intuition? Explain xx pts) The xxxxx of xxxxxx xxxxxx two xxxxxxxx deviations of xxx mean is:14 xx 2*(6 xxxxx x (1 xxxx 26 083)Since xxx of the xxxxxx are xx xxxx interval, xxxxx are no xxxxxx that would xx considered xxxxxxx xx inspection, xxxx of the xxxxxx appear to xx unusual, xx xxxx result xxxx notdiffer from xx intuition Refer xx the xxxxxxxxx xxxxx for xxxxxxxxx 9, 10, xxx 11 Show xxx work xxxx.....
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