Question

44% of men have considered themselves professional baseball fans. You randomly select 10 men and ask each if he considers himself a professional baseball fan. Find the probability that the number who consider themselves baseball fans is? (a) exactly? five, (b) at least? six, and? (c) less than four

Answer #1

X ~ Binomial (n,p)

Where n = 10 , p = 0.44

The binomial probability distribution is

P(X) = ^{n}C_{x} p^{x} ( 1 -
p)^{n-x}

a)

P( X = 5) = ^{10}C_{5} 0.44^{5}
0.56^{5}

= **0.2289**

b)

P( X >= 6) = P( X = 6) +P( X = 7) +P( X = 8) +P( X = 9) +P( X = 10)

= ^{10}C_{6} 0.44^{6} 0.56^{4}
+^{10}C_{7} 0.44^{7} 0.56^{3}
+^{10}C_{8} 0.44^{8} 0.56^{2}
+^{10}C_{9} 0.44^{9} 0.56
+^{10}C_{10} 0.44^{10} 0.56^{0}

= **0.2407**

c)

P( X < 4) = P( X <= 3)

= P( X = 0) + P( X = 1) + P( x = 2) + P( X 3)

= ^{10}C_{0} 0.44^{0} 0.56^{10}
+^{10}C_{1} 0.44^{1} 0.56^{9}
+^{10}C_{2} 0.44^{2} 0.56^{8}
+^{10}C_{3} 0.44^{3} 0.56^{7}

= **0.2877**

43%
of men consider themselves professional baseball fans. You randomly
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themselves baseball fans is (a) exactly five (b) at least six (c)
less than four.

3. 37% of women consider themselves professional baseball fans.
You randomly select 6 women and ask each if she considers himself a
professional baseball fan. Find the probability that the number who
consider themselves baseball fans is
(a) exactly four
(b) at least three
(c) less than two

37% of women consider themselves professional baseball fans. You
randomly select 6 women and ask each if she considers himself a
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36 % of men think of themselves fans of professional baseball.
You randomly select six men and ask each if he considers himself a
fan of professional baseball. Complete parts (a) through (d)
below.
(a) Find the mean of the binomial distribution.
(b) Find the variance of the binomial distribution.
(c) come up with the standard deviation of the binomial
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(d) Interpret the end result in the context of the real-life
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*4.2.27
37
%
of women consider themselves fans of professional baseball. You
randomly select six women and ask each if she considers herself a
fan of professional baseball. Complete parts (a) through (d)
below.
(a) Find the mean of the binomial distribution.
mu
equals2.2
(Round to the nearest tenth as needed.)
(b) Find the variance of the binomial distribution.
sigma
squaredequals1.4
(Round to the nearest tenth as needed.)
(c) Find the standard deviation of the binomial
distribution.
sigma
equals1.2
(Round...

3737%
of women consider themselves fans of professional baseball. You
randomly select six women and ask each if she considers herself a
fan of professional baseball. Complete parts (a) through (c)
below.(a) Construct a binomial distribution using
n equals 6n=6
and
p equals 0.37p=0.37.
x
P(x)
0
0.0630.063
1
0.2200.220
2
0.3230.323
3
0.2530.253
4
0.1120.112
5
0.0260.026
6
0.0030.003
(Round to the nearest thousandth as needed.)
(b) Graph the binomial distribution using a histogram and
describe its shape. Choose...

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56% of us adults have very little confidence in
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a P(5) round to 3 decimal place

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