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Chapter 11, Problem 7RE(choose chapter or problem)
Driving Age According to a Gallup poll, 60% of U.S. women 18 years old or older stated that the minimum driving age should be 18. In a random sample of 15 U.S. women 18 years old or older, find the probability that:
(a) Exactly 10 believe that the minimum driving age should be 18.
(b) Fewer than 5 believe that the minimum driving age should be 18.
(c) At least 5 believe that the minimum driving age should be 18.
(d) Between 7 and 12, inclusive, believe that the minimum driving age should be 18.
(e) In a random sample of 200 U.S. women 18 years old or older, what is the expected number who believe that the minimum driving age should be 18? What is the standard deviation?
(f) If a random sample of 200 U.S. women 18 years old or older resulted in 110 who believe that the minimum driving age should be 18, would this be unusual? Why?
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QUESTION:
Driving Age According to a Gallup poll, 60% of U.S. women 18 years old or older stated that the minimum driving age should be 18. In a random sample of 15 U.S. women 18 years old or older, find the probability that:
(a) Exactly 10 believe that the minimum driving age should be 18.
(b) Fewer than 5 believe that the minimum driving age should be 18.
(c) At least 5 believe that the minimum driving age should be 18.
(d) Between 7 and 12, inclusive, believe that the minimum driving age should be 18.
(e) In a random sample of 200 U.S. women 18 years old or older, what is the expected number who believe that the minimum driving age should be 18? What is the standard deviation?
(f) If a random sample of 200 U.S. women 18 years old or older resulted in 110 who believe that the minimum driving age should be 18, would this be unusual? Why?
ANSWER:Step 1 of 2 :
According to a Gallup poll, 60% of U.S. women 18 years old or older stated that the minimum driving age should be 18. In a random sample of 15 U.S. women 18 years old or older, find the probability that.
\(X \sim\) binomial distribution with parameters n and p.
Where , n=15 and p=60%=0.6.
a) Exactly 10 believe that the minimum driving age should be 18.
\(\begin{array}{l} \mathrm{P}(\mathrm{x})={ }^{n_{c}}{ }_{x} p^{x} q^{n-x} ; \text { where, } \mathrm{q}=1-\mathrm{p} . \\ \begin{aligned} \mathrm{P}(\mathrm{x}=10)=15 c_{10}(0.6)^{10 *}(1-0.6)^{15-10}=3003^{*} 0.006{ }^{*} 0.01024 \\ \mathrm{P}(\mathrm{X}=10)=0.1859 . \end{aligned} \end{array}\)
b) Fewer than 5 believe that the minimum driving age should be 18.
\(\begin{array}{l} \mathrm{P}(\mathrm{X}<5)=\mathrm{P}(\mathrm{x}=1)+\mathrm{P}(\mathrm{x}=2)+\mathrm{P}(\mathrm{x}=3)+\mathrm{P}(\mathrm{x}=4) \\ =15 c_{1} \\ (0.6)^{1 *}(1-0.6)^{15-1}+15 c_{2}(0.6)^{2} *(1-0.6)^{15-2}+15 c_{3}(0.6)^{3} *(1-0.6)^{15-3}+15 c_{4}(0.6)^{4} *(1-0.6)^{15-4} \\ =0.000024+0.00025+0.0016+0.0074 \\ =0.0093 \\ \mathrm{P}(\mathrm{X}<5)=0.0093 \end{array}\)
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