# Mathematics

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

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

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

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

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%

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

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

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

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

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

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%

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

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.

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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