Question

A random sample of hybrid vehicle fuel consumptions has a sample mean of x¯=53.2 mpg and sample standard deviation of s=4.8 mpg. Use the Empirical Rule to estimate the percentage of hybrid vehicle fuel consumptions that are less than 43.6 mpg. Round your answer to the nearest tenth.

Answer 1

Answer:

2.5%

Step-by-step explanation:

Since the mean is 53.2, a fuel consumption of 43.6 mpg is 53.2−43.6=9.6 mpg less than the mean, which is 2 standard deviations.

By the Empirical Rule, we know that about 95% of the data lies within 2 standard deviations of the mean. Therefore, 100%−95%=5% of the data lie more than 2 standard deviations away from the mean.

Since the distribution of hybrid vehicle fuel consumptions is symmetric, about half of the remaining 5% will lie to either extreme. So about 2.5% of fuel consumptions are less than 43.6 mpg.

Answer 2

The normal distribution is a symmetric probability distribution about the mean. The percentage of hybrid vehicle fuel consumption that is less than 43.6 mpg is 2.5%.

What is Normal Distribution?

The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.

Given that the mean is 53.2, while the standard deviation is 4.8 mpg. Therefore, Accoding to the emperical rule, we can write the values as,

μ+3σ = 67.6

μ+2σ = 62.8

μ+σ = 58

μ = 53.2

μ-σ = 48.4

μ-2σ = 43.6

μ-3σ = 38.8

Therefore, The percentage of hybrid vehicle fuel consumption that is less than 43.6 mpg is,

Percentage = (0.15 + 2.35)% = 2.5%

Hence, The percentage of hybrid vehicle fuel consumption that is less than 43.6 mpg is 2.5%.

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