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Nitella [24]
3 years ago
12

The miles-per-gallon obtained by the 1995 model q cars is normally distributed with a mean of 22 miles-per-gallon and a standard

deviation of 5 miles-per-gallon. what is the probability that a car will get less than 21 miles-per-gallon? (4 decimal format = 0.0000)

Mathematics
2 answers:
nikitadnepr [17]3 years ago
5 0

Answer:

The probability that a car will get less than 21 miles-per-gallon is 0.4207.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 22, \sigma = 5

What is the probability that a car will get less than 21 miles-per-gallon?

This probability is the pvalue of Z when X = 21. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{21 - 22}{5}

Z = -0.2

Z = -0.2 has a pvalue of 0.4207.

So the probability that a car will get less than 21 miles-per-gallon is 0.4207.

mina [271]3 years ago
4 0
That probability is about 0.4207.

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