Answer:
Step-by-step explanation:
Given that average or mean score on a driving exam by a group of driver's education students is 80 points, and standard deviation 3 points.
We are asked to apply Chebychev's theorem for this.
This theorem states that if x is an integrable random variable with mean = mu and std dev = sigma then
P(|X-\mu |>= k\sigma )<= {\frac {1}{k^{2}}}.
Substitute our values here.
P(|x-80|>=2(3)|<= 1/4
|x-80|>=6 mean
x is eithre less than 80-6 or greater than 80+6
i.e. probability for driving educated students getting scores not between
74 and 86 is less than 0.25
Using chebyshev's theorem, the proportion of the samples which falls within 2 standard deviation from the mean is 75%
Recall :
For k = 2
The percentage of observations which falls within 2 standard deviations from the mean is :
1 - (1/2²)
1 - 1/4 = 0.75
Hence, (0.75 × 100%) = 75% of the distribution falls within 2 standard deviation from the mean.
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