$\bf \qquad \qquad \textit{direct proportional variation}\\\\
\textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------\\\\
(\stackrel{x}{8}~~,~~\stackrel{y}{4})\implies 
\begin{cases}
x=8\\
y=4
\end{cases}\implies 4=k8\implies \cfrac{4}{8}=k\implies \cfrac{1}{2}=k
\\\\\\
\boxed{y=\cfrac{1}{2}x}$

6 0

3 years ago

When Carson runs the 400 meter dash, his finishing times are normally distributed with a mean of 65 seconds and a standard devia

just olya [345]

Given Information:

Mean time to finish 400 meter dash = μ = 65 seconds

Standard deviation to finish 400 meter dash = σ = 2.5 seconds

Confidence level = 95%

Required Information:

95% confidence interval = ?

Answer:

$CI = 60 \: to \: 70 \: seconds$

Step-by-step explanation:

In the normal distribution, the empirical rule states approximately 68% of all the data lie within 1 standard deviation from the mean, approximately 95% of all the data lie within 2 standard deviations from the mean and approximately 99.7% of all the data lie within 3 standard deviations from the mean.

The confidence interval for 95% confidence limit is given by

$CI = \mu \pm 2\sigma$

Since approximately 95% of all the data lie within 2 standard deviations from the mean. μ is the mean time Carson takes to finish 400 meter dash and σ is the standard deviation.

$CI = 65 \pm 2(2.5)$