2. For a particular model of a car, a dealer offers 3 sizes of engines, 2 types of stereos, 18 body

Mathematics

1 answer:

Gnesinka [82]3 years ago

3 0

The given details follow the product rule. The different model of the car available are 756.

Given that:

$Engines = 3$

$Stereos = 2$

$Body=18$

$Color = 7$

The different possibility is calculated using the following product rule:

$Total =Engines \times Stereos \times Body \times Color$

So, we have:

$Total = 3\times 2\times 18 \times 7$

$Total = 756$

Hence, there are 756 different models available.

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Use the normal approximation to the binomial distribution to answer this question. Fifteen percent of all students at a large un

spayn [35]

Answer:

60.26% probability that less than twenty students are absent

Step-by-step explanation:

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 $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .