Lesson 127

Example 1
Classify a Data Distribution Determine whether the data {112, 106, 106, 110, 107, 107, 112, 109, 106, 108, 109, 110, 111, 106, 107, 108, 106, 106, 111, 109, 110, 108, 110, 106, 106, 107, 106, 108, 106, 107, 107, 110, 107, 108, 107, 108, 109, 108, 109, 109 } appear to be positively skewed, negatively skewed, or normally distributed. Make a frequency table for the data. Then use the table to make a histogram. Value Frequency 112 2
Since the histogram is high at the left, and has a tail to the right, the data are positively skewed.

Example 2

Normal Distribution BUSINESS A homebased business found that the lengths of 5500 of their special candy canes for the holidays are normally distributed with a mean length of 20 centimeters and a standard deviation of 0.5 centimeters. a. About how many of the candy canes were between 19.5 and 20.5 centimeters in length? Draw a normal curve. Label the mean and the mean plus or minus multiples of the standard deviation. The values of 19.5 and 20.5 are 1 standard deviation below and above the mean, respectively. Therefore, about 68% of the data are between 19.5 and 20.5. 5500 x 68% = 3740 Multiply 5500 by 0.68. About 3740 of the candy canes are between 19.5 and 20.5 centimeters in length.
b. What is the probability that a candy cane selected at random had a length less than 19 cm? The value of 19 is two standard deviations below the mean. You know that about 100% 95% or 5% of the data are more than two standard deviations away from the mean. By the symmetry of the normal curve, half of 5%, or 2.5%, of the data are more than two standard deviations below the mean. The probability that a candy cane selected at random had a length less than 19 cm is about 2.5% or 0.025.

C L C D B W P U X W R Z A Z C
A I O A R D O B C U T P T G O
N G M E W E I R D R F C N T O
D H E R S Y C O K Y E I A N K
Y T T B R N L N L S K C S E I
C S S R C P O I A C H H N M E
A R E E H H M I O R E O V A S
N M L G V A I T T I P I P N D
E N M N F L S M M A X T J R S
S L E I G H E I N E R I R O L
H R P G V M S Z N E N O U E L
E L O P H T R O N G Y N C W E
T H G J L S U A L C B N R E B
D Q O E D Z R E I N D E E R D
W A T H K N E Z T I L B H G J
O O H A O C A R O L S T S I J
E Y L L O H C U P I D H A F D
R E N N O D O Y L L O J D T A
bells Blitzen candy cane carols chimney Claus Comet cookies Cupid Dancer Dasher decorations
Donner elves family gift gingerbread Ho ho ho holly jingle jolly lights merry mistletoe
North Pole ornament Prancer reindeer Rudolph Santa sleigh stocking tree Vixen workshop
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