ull Ultra 3:59 PM @ 92%.-. + 1. For the following data set Data: 10 15 30 30 31

Question

ull Ultra 3:59 PM @ 92%.-. + 1. For the following data set Data: 10 15 30 30 31 31 32 32 33 33 34 36 38 39 40 40 41 41 41 42 42 42 42 43 43 43 43 44 44 45 45 46 46 47 47 48 48 48 60 70 a. Make a frequency diagram with eight classes. b. Make a histogram c. Make a Stem and Leaf diagram. d. Give the five number summary and e. Draw the box and whisker diagram showing possible outliers. 5 points 5 points 2.5 points 2.5 points 5 points a. Frequency Diagram Classes Frequency Relative Fregquency Totals 2. It is known that 68% of college students like rap music. In a group of 52 students, find the probability that: a) Exactly 34 like rap music. b)Between 30 and 40 (inclusive) like rap music.. c) Less than 32 like rap music. 5 poir More than 34 like rap music. 5 poi Answer all ASAP

Explanation / Answer

2.

BIONOMIAL DISTRIBUTION
pmf of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
where
k = number of successes in trials   
n = is the number of independent trials   
p = probability of success on each trial
I.
mean = np
where
n = total number of repetitions experiment is excueted
p = success probability
mean = 52 * 0.68
= 35.36
II.
variance = npq
where
n = total number of repetitions experiment is excueted
p = success probability
q = failure probability
variance = 52 * 0.68 * 0.32
= 11.3152
III.
standard deviation = sqrt( variance ) = sqrt(11.3152)
=3.3638
a.
P( X = 34 ) = ( 52 34 ) * ( 0.68^34) * ( 1 - 0.68 )^18
= 0.1067
b.
NORMAL APPROXIMATION TO BINOMIAL DISTRIBUTION
the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
mean ( np ) = 52 * 0.68 = 35.36
standard deviation ( npq )= 52*0.68*0.32 = 3.3638
equation of the normal curve is ( Z )= x - u / sd/sqrt(n) ~ N(0,1)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 30) = (30-35.36)/3.3638
= -5.36/3.3638 = -1.5934
= P ( Z <-1.5934) From Standard Normal Table
= 0.05553
P(X < 40) = (40-35.36)/3.3638
= 4.64/3.3638 = 1.3794
= P ( Z <1.3794) From Standard Normal Table
= 0.91611
P(30 < X < 40) = 0.91611-0.05553 = 0.8606
c.
P( X < 32) = P(X=31) + P(X=30) + P(X=29) + P(X=28) + P(X=27) + P(X=26) + P(X=25) + P(X=24) + P(X=23) + P(X=22)
= ( 52 31 ) * 0.68^31 * ( 1- 0.68 ) ^21 + ( 52 30 ) * 0.68^30 * ( 1- 0.68 ) ^22 + ( 52 29 ) * 0.68^29 * ( 1- 0.68 ) ^23 + ( 52 28 ) * 0.68^28 * ( 1- 0.68 ) ^24 + ( 52 27 ) * 0.68^27 * ( 1- 0.68 ) ^25 + ( 52 26 ) * 0.68^26 * ( 1- 0.68 ) ^26 + ( 52 25 ) * 0.68^25 * ( 1- 0.68 ) ^27 + ( 52 24 ) * 0.68^24 * ( 1- 0.68 ) ^28 + ( 52 23 ) * 0.68^23 * ( 1- 0.68 ) ^29 + ( 52 22 ) * 0.68^22 * ( 1- 0.68 ) ^30
= 0.1265
d.
P( X < = 34) = P(X=34) + P(X=33) + P(X=32) + P(X=31) + P(X=30) + P(X=29) + P(X=28) + P(X=27) + P(X=26) + P(X=25) + P(X=24)  
= ( 52 34 ) * 0.68^34 * ( 1- 0.68 ) ^18 + ( 52 33 ) * 0.68^33 * ( 1- 0.68 ) ^19 + ( 52 32 ) * 0.68^32 * ( 1- 0.68 ) ^20 + ( 52 31 ) * 0.68^31 * ( 1- 0.68 ) ^21 + ( 52 30 ) * 0.68^30 * ( 1- 0.68 ) ^22 + ( 52 29 ) * 0.68^29 * ( 1- 0.68 ) ^23 + ( 52 28 ) * 0.68^28 * ( 1- 0.68 ) ^24 + ( 52 27 ) * 0.68^27 * ( 1- 0.68 ) ^25 + ( 52 26 ) * 0.68^26 * ( 1- 0.68 ) ^26 + ( 52 25 ) * 0.68^25 * ( 1- 0.68 ) ^27 + ( 52 24 ) * 0.68^24 * ( 1- 0.68 ) ^28  
= 0.3928
P( X > 34) = 1 - P ( X <=34) = 1 -0.3928 = 0.6072

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