# Mathematics

**STAT 200 QUIZ 2 WEEKS 3, 4, 5, 6 (16 @ 0.5 pts = 8 points)**

**SHOW YOUR CALCULATIONS NOT SOFTWARE**

**SUBMIT ANSWER SHEET ONLY NOT THESE QUIZ PROBLEMS**

**1. For a set of numbers, if the mean is equal to the median, its distribution might be:**

**a. Right-skewed**

**b. Left-skewed**

**c. Normally distributed**

**d. Positively-skewed**

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**2. In the graph, there are two distrubitions and we can tell (Select ALL that apply):**

**a. The mean of distribution A> the mean of distribution B**

**b. The mean of distribution A < the mean of distribution B**

**c. The standard deviation of distribution A> the std deviation of distribution B**

**d. The standard deviation of distribution A= the st deviation of distribution B**

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**3. (T/F) A BOX PLOT gives us considerable information about a data set, including the number of data points in any given range.**

**4. There are 20 coupons rolled up and placed inside round plastic balls in a box. There are 3 different types of coupons: 10 of them can be redeemed for “free drinks”, 5 can be redeemed for “free desserts”, and 5 can be redeemed for “free entrees”. If you shake the box and then randomly select one coupon. What’s the probability that you will get a “free entree coupon”? (a) 25% (b) 10% (c) 20% (d) 50% (e) None of these**

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**5. Mary was tossing a coin. She tossed three times. What’s the probability that at the first toss she gets a head, the second toss she gets a tail at and the third time she get a tail? (a) 3/8 (b) 0.50 (c) 12.5% (d) 25%**

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**6. 100,000 people: twenty percent are children younger and 7% of those children are malnourished. How many children malnourished? (a) 1000 (b) 1400 (c) 1200 (d) 1600**

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**7. A normal distribution of data points has a mean of 15 and a standard deviation of 5. What is the standardized Z-VALUE for a data point with a value of 7? (a) +1.3 (b) -1.6 (c) -2.1 (d) +1.6**

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**8. In this data set above, what is the probability that a data point is 7 or less?**

**(a) 4.5% (b) 0.095 (c) 0.055 (d) 55%**

**9. TOSSING A COIN: Using the Normal to approximate the Binomial (NOT the complex formulas) with a What is the probability of (binomial) data getting 17 to 21 heads out of 36 tosses? THE RANGE FOR WHICH WE DETERMINE THE Z VALUES FOR THE LOW AND HIGH ENDS IS?**

**(a) 17 to 21 (b) 17.5 to 19.5 (c) 16 to 22 (d) 16.5 to 21.5**

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**10. What are the MEAN and Standard deviation approximations we use for this calculation?**

**(a) 18 and 3 (b) 17 and 10 (c) 18 and 9 (d) 16 and 3 (e) None of these**

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**11. What are the z-Values that correspond to the range you determined in #9 above?**

**(a) +0.5 and -1.17 (b) -0.5 and +1.17 (c) – 0.16 and +0.38 (d) none of these**

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**12. For these z-Values from #11, what are the areas (probabilites) to the LEFT ?**

**(a) 0.3085 and 87.9% (b) 3.85% and 0.0879 (c) 0.4801 and 13% (d) 4.81% and 95.2%**

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**13. FINALLY, what is the approximate probability of 17 to 21 heads out of 35 coin tosses using the Normal to approximate the Binomial?**

**(a) 67% (b) 57% (c) 0.43 (d) 0.057 (e) None of these**

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**14. CONFIDENCE INTERVALS IF WE HAVE THE MEAN BUT NOT THE STANDARD DEVATION WE USE THE _______, BUT IF WE HAVE THE MEAN AND THE STANDARD DEVAITION WE USE THE _________**

**(a) z-Tables and t-Tables (b) t-Tables and z-Tables (c) neither, we can’t calculate a confidence interval. **

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**15. Using the t-Tables with an ****α**** of 5% the Confidence Interval would have limits at:**

**(a) 5% and 95% (b) 0.025 and 0.975 (c) 1% and 99% (d) none of these**

**16. Calculate the 99% Confidence Interval for 41 sample data points with a mean (m) of 25 and a standard deviation (s) of 5**

**(a) 21 to 29 (b) 23 to 27 (c) 24 to 26 (d) 22.5 to 27.5**

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