Please answer the following questions and show all work please.
Refer to the following frequency distribution for Questions 1, 2, 3, and 4.
The frequency distribution below shows the distribution for suspended solid concentration (in ppm) in river water of 50 different waters collected in September 2011.
Concentration (ppm) Frequency
20 - 29 1
30 - 39 8
40 - 49 8
50 - 59 10
60 - 69 12
70 - 79 7
80 - 89 2
90 - 99 2
1. What percentage of the rivers had suspended solid concentration greater than or equal to 70?
2. Calculate the mean of this frequency distribution.
3. In what class interval must the median lie? Explain your answer. (You don’t have to find the median)
4. Assume that the smallest observation in this dataset is 20. Suppose this observation were incorrectly recorded as 2 instead of 20. Will the mean increase, decrease, or remain the same? Will the median increase, decrease or remain the same? Explain.
Refer to the following information for Questions 5 and 6.
A coin is tossed 4 times. Let A be the event that the first toss is heads. Let B be the event that the third toss is heads.
5. What is the probability that the third toss is heads, given that the first toss is heads?
6. Are A and B independent? Why or why not?
Refer to the following data to answer questions 7 and 8. Just the answer
A random sample of song playing times in seconds is as follows:
242 231 220 213 230 293
7. Find the standard deviation.
8. Are any of these playing times considered unusual in the sense of our textbook? Explain. Does this differ with your intuition? Explain.
Refer to the following situation for Questions 9, 10, and 11.
The boxplots below show the real estate values of single family homes in two neighboring cities, in thousands of dollars.
For each question, give your answer as one of the following: (a) Tinytown; (b) BigBurg; (c) Both cities have the same value requested; (d) It is impossible to tell using only the given information. Please explain answer in each case.
9. Which city has greater variability in real estate values?
10. Which city has the greater percentage of households with values $85,000 and over?
11. Which city has a greater percentage of homes with real estate values between $55,000 and $85,000?
12. A random sample of the lifetime of 49 UltraIllum light bulbs has a mean of 3,960 hours and a standard deviation of 200 hours. Construct a 95% confidence interval estimate of the mean lifetime for all UltraIllum light bulbs.
Refer to the following information for Questions 13 and 14.
There are 500 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 95 people; the roster of the Statistics class shows 86 people. There are 43 overachieving seniors on both rosters.
13. What is the probability that a randomly selected senior is in exactly one of the two classes (but not both)?
14. If the student is in the Statistics class, what is the probability the student is also in the Calculus class?
Refer to the following information for Questions 15, 16, and 17.
Consider the following situation for Questions 20 and 21.
Airline overbooking is a common practice. Due to uncertain plans, many people cancel at the last minute or simply fail to show up. Air Eagle is a small commuter airline. Its past records indicate that 80% of the people who make a reservation will show up for the flight. The other 20% do not show up. Air Eagle decided to book 12 people for today’s flight. Today’s flight has just 10 seats.
20. Find the probability that there are enough seats for all the passengers who show up. (Hint: Find the probability that in 12 people, 10 or less show up.)
21. How many passengers are expected to show up?
22. Given a sample size of 65, with sample mean 726.2 and sample standard deviation 85.3, we perform the following hypothesis test.
What is the conclusion of the test at the level? Explain
Refer to the following information for Questions 23, 24, and 25.
The BestEver credit scores are normally distributed with a mean of 600 and a standard deviation of 100.
23. What is the probability that a randomly person has a BestEver credit score between 500 and 700?
24. Find the 90th percentile of the BestEver credit score distribution.
25. If a random sample of 100 people is selected, what is the standard deviation of the sample mean BestEver credit scores?
27. A certain researcher thinks that the proportion of women who say that female bosses are harshly critical is greater than the proportion of men.
In a random sample of 200 women, 27% said that female bosses are harshly critical.
In a random sample of 220 men, 25% said that female bosses are harshly critical.
At the 0.05 significance level, is there sufficient evidence to support the claim that the proportion of women saying female bosses are harshly critical is higher than the proportion of men saying female bosses are harshly critical?
28. Randomly selected nonfatal occupational injuries and illnesses are categorized according to the day of the week that they first occurred, and the results are listed below. Use a 0.05 significance level to test the claim that such injuries and illnesses occur with equal frequency on the different days of the week. Justify answer.
Day Mon Tue Wed Thu Fri
Number 23 23 21 20 18
29. Is there a linear correlation between x and y at the 0.01 significance level? Justify your answer.
30. Find an equation of the least squares regression line. Show all work please.
x 0 ??" 1 1 1 2
y 2 ??" 2 5 4 6
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