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iVinArrow [24]
4 years ago
8

insurance company checks police records on 559 accidents selected at random and notes that teenagers were at the wheel in 91 of

them. Use this information to complete parts a through d below.​a) Create a​ 95% confidence interval for the percentage of all auto accidents that involve teenage drivers.​(nothing​%,nothing​%)
Mathematics
1 answer:
ss7ja [257]4 years ago
7 0

Answer: (13.22\%,\ 19.34\%)

Step-by-step explanation:

Given : Sample space : n= 559

Sample proportion : \hat{p}=\dfrac{91}{559}=0.162790697674\approx0.1628

=16.28\%

Significance level : \alpha= 1-0.95=0.05

Critical value : z_{\alpha/2}=1.96

Confidence level for population proportion:-

\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\=0.1628\pm (1.96)\sqrt{\dfrac{0.1628(1-0.1628)}{559}}\\\\=0.1628\pm0.030604971367\\\\\approx 0.1628\pm0.0306=(0.1322,\ 0.1934)=(13.22\%,\ 19.34\%)

Hence, 95% confidence interval for the percentage of all auto accidents that involve teenage drivers.= (13.22\%,\ 19.34\%)

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a person kicks a ball from the ground into the air with an initial upward velocity of 8 feet per second. what is the maximum hei
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\bf ~~~~~~\textit{initial velocity}
\\\\
\begin{array}{llll}
~~~~~~\textit{in feet}
\\\\
h(t) = -16t^2+v_ot+h_o
\end{array} 
\quad 
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v_o=\stackrel{8}{\textit{initial velocity of the object}}\\\\
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h=\stackrel{}{\textit{height of the object at "t" seconds}}
\end{cases}
\\\\\\
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now let's find the y-coordinate of its vertex

\bf \textit{vertex of a vertical parabola, using coefficients}
\\\\
h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+8}t\stackrel{\stackrel{c}{\downarrow }}{+0}
\qquad \qquad 
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\\\\\\
\left(\qquad ,~~0-\cfrac{8^2}{4(-16)}  \right)\implies (\quad ,~0+1)\implies (\quad ,~1)

when will it hit the ground?

\bf \stackrel{h(t)}{0}=-16t^2+8t\implies 16t^2-8t=0\implies 8t(2t-1)=0
\\\\\\
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\\\\\\
2t-1=0\implies 2t=1\implies \stackrel{\textit{half a second later it  when it came back down}}{t=\cfrac{1}{2}}

3 0
3 years ago
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