Is this proportional

Mathematics

1 answer:

emmasim [6.3K]3 years ago

6 0

Answer:

Yes

Step-by-step explanation:

For every 1/2 mile, it takes 1/4 hour. For the 1 mile, this is double the 1/2 mile, so the hours should be double the 1/4 hour. This is true because 1/2=2/4 and 2 times 1/4, or 1/4• 2 equals 2/4. It is the same idea for the 3rd row.

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According to a 2009 Reader's Digest article, people throw away approximately 11% of what they buy at the grocery store. Assume t

expeople1 [14]

Answer:

0.14% probability that the sample proportion exceeds 0.2

Step-by-step explanation:

I am going to use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

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.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .