Statistics
Chelsea29440
Statisticsmidterm.xlsxChapter 1.1 (20 points)
| 1. Based on the data below, answer the following questions: | |||
| Age | Frequency | Relative Frequency | Cumulative Relative Frequency |
| < 18 | 5 | ||
| 18 - 25 | 43 | ||
| 26 - 33 | 134 | ||
| 34 - 41 | 128 | ||
| 42 - 49 | 160 | ||
| 50 - 57 | 85 | ||
| 58 - 65 | 51 | ||
| 65 - 70 | 34 | ||
| > 70 | 10 | ||
| *Use 4 decimal places for Frequency and Relative Frequency on the table | |||
| **You may round up to 2 decimal places for final results | |||
| a. Complete the table | |||
| b What is the total frequency? | |||
| c. What is the mean of all frequencies? | |||
| d. What is the frequency for ages 50-57? | |||
| e. What is the relative frequency for ages 65-70? | |||
| f. What is the relative frequency for ages over 41? | |||
| g. What is the relative frequency for ages below 50? | |||
| h. What is the cumulative relative frequency for ages below 26? | |||
| i. What is the cumulative relative frequency for ages 42-49? | |||
| j. Insert a bar graph for the relative frequency column and tell me what it resembles. Instructions to insert a bar chart are below. | |||
| How to insert a bar chart? | |||
| 1. Select the column required to be depicted; you may include the header | |||
| 2. Go to the Insert tab | |||
| 3. Search for insert column or bar chart in the Charts ribbon | |||
| 4. Choose either 2D or 3D vertical bars |
Chapter 1.2 (5 pts)
| 2 - In full sentences, provide me 2 examples of quantiative discrete, 2 examples of quantitative continuous and 1 example of qualitative data below. For example, "My doctor told me to increase my Vitamin D intake to 2 pills instead of 1." |
| Quantitative Discrete |
| Quantitative Discrete |
| Quantitative Continuous |
| Quantitative Continuous |
| Qualitative |
Chapter 2 (15 pts)
| 3. You have been provided the following values: | ||||
| 23 | 23 | 15 | 19 | 14 |
| 21 | 48 | 32 | 32 | 32 |
| 59 | 22 | 62 | 29 | 9 |
| a. Construct a stem-and-leaf plot. | ||||
| b. How many "stems" are in your plot? | ||||
| c. Is the data skewed to the left or to the right? | ||||
| d. What is the mean? | ||||
| e. What is the median? | ||||
| f. What is the mode? | ||||
| g. What is the standard deviation? | ||||
| h. Calculate 1.s.d. below the mean. | ||||
| i. Calculate 1 s.d. above the mean. | ||||
| j. Calculate 2 s.d. below the mean. | ||||
| k. Calculate 2 s.d. above the mean. | ||||
| l. Calculate 3 s.d. below the mean. | ||||
| m. Calculate 3 s.d. above the mean. | ||||
| n. Are there any outliers in the data? | ||||
| o. If you answered yes to the question above, which one (s)? |
Chapter 3.1 (10 pts)
| 4. Answer the following probabilities: |
| a. A die is thrown once. What is the probability that the score is a factor of 6? |
| b. A fair coin is tossed three times. What is the probability of obtaining one Head and two Tails? |
| (A fair coin is one that is not loaded, so there is an equal chance of it landing Heads up or Tails up.) |
| c. There are 10 counters in a bag: 3 are red, 2 are blue and 5 are green. |
| The contents of the bag are shaken before Maxine randomly chooses one counter from the bag. |
| What is the probability that she doesn't pick a red counter? |
| d. A man chooses a card at random from a deck of cards. |
| What is the probability that the card is a diamond? |
| e. A man chooses a card at random from a deck of cards. |
| What is the probability that the card is a queen of diamonds? |
Chapter 3.2 (10 pts)
| 5. The table below lists situation in numbers by WHO regions as of May 27, 2020: | |||
| Country, Other | Cases | Deaths | TOTAL CASES |
| Africa | 85,815 | 2,308 | |
| Americas | 2,495,924 | 2,641,734.00 | |
| Eastern Mediterranean | 11,452 | 461,042.00 | |
| Europe | 2,061,828 | 2,238,054.00 | |
| South-East Asia | 6,359 | 224,882.00 | |
| Western Pacific | 176,404 | 6,927 | |
| TOTALS | 27,046 | 5,837,166.00 | |
| a. Complete the totals. | |||
| b. What is the probability that a randomly selected person in the Americas? | |||
| c. What is the probability that a randomly selected person in Europe? | |||
| d. What is the probability that a randomly selected person has died of COVID-19? | |||
| e. What is the probability that a randomly selected person is a confirmed case of COVID-19? | |||
| f. What is the probability that a randomly selected person has been either in the America or Europe? | |||
| g. What is the probability that a randomly selected person has neither been in Europe nor in South-East Asia? | |||
| h. What is the probability that a randomly selected person has COVID-19 and is in Western Pacific? | |||
| i. What is the probability that a randomly selected person has died and was in Eastern Mediterranean? | |||
| j. What is the complement of a random selected person not being in the Americas? |
Chapter 4 (15 pts)
| 6. You have been provided the following probability distribution: | |||
| Pets | P(x) | x*P(x) | (x-µ)²P(x) |
| 0 | 0.330 | ||
| 1 | 0.270 | ||
| 2 | 0.300 | ||
| 3 | 0.050 | ||
| 4 | 0.025 | ||
| 5 | 0.020 | ||
| 6 or more | 0.005 | ||
| Let x = the total number of pets in a household | |||
| a. Complete table | |||
| b. What is the probability of a household having no pets? | |||
| c. What is the probability of a household having exactly 3 pets? | |||
| d. What is the probability of a household having between 1 and 3 pets? | |||
| e. What is the probability of a household having more than 5 pets? | |||
| f. On average, how many pets does a household have? | |||
| g. Calculate the standard deviation. | |||
| h. What is 1 standard deviations below the mean? | |||
| i. What is 1.5 standard deviations above the mean? | |||
| j. What is 3 standard deviations above the mean? |
Chapter 5 (10 pts)
| 7. Find the probability that x falls in the shaded area (2.5 pts) | |||||||||
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | |||
| 8. For the continuous probability distribution below, what is P(x = 3)? (2.5 pts) | |||||||||
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | |||
| 9. Identify the following values: (5 pts) | |||||||||
| a. Lowest value | |||||||||
| b. Highest value | |||||||||
| c. Height of the rectangle | |||||||||
| d. Label of x-axis (words) | |||||||||
| e. Probability that x falls in the shaded area | |||||||||
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | |||
Chapter 6 (15 pts)
| 10. A survey was conduted and results are normally distributed. The mean is 33 with a known standard deviation of 17. Calculate the z scores below and the probabilties | ||
| z score | Probability | |
| a. Find the probability that x < 36? | ||
| b. Find the probability that x > 43? | ||
| c. Find the probability that x < 35? | ||
| d. Find the probability that x is between 40 and 48? | ||
| e. Find the probability that x is between 22 and 25? | ||
Extra Credit (10 points)
| You have calculated the z values and probabilities on chapter 6 problem |
| Your extra credit is to draw the normal distribution curve (bell curve) for each problem (a-e) by adding all values, labeling it and adding shaded areas |
