Mathematics, 24.03.2020 20:13 alexisbreton

Consider the probability that fewer than 20 out of 155 people have been in a car accident. Assume the probability that a given person has been in a car accident is 10%. Approximate the probability using the normal distribution. Round your answer to four decimal places.

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Answer from: 133596

0.8264 = 82.64% probability that fewer than 20 out of 155 people have been in a car accident.

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

In this problem, we have that:

n = 155, p = 0.1

$\mu = E(X) = np = 155*0.1 = 15.5$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{155*0.1*0.9} = 3.735$

Consider the probability that fewer than 20 out of 155 people have been in a car accident.

The number of people that have been in a car acident is a discrete value, so fewer than 20 is 19 or less.

This probability is the pvalue of Z when X = 19.

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

$Z = \frac{19 - 15.5}{3.735}$

Z = 0.94

Z = 0.94 has a pvalue of 0.8264

0.8264 = 82.64% probability that fewer than 20 out of 155 people have been in a car accident.

Answer from: Quest

the highest percentage for deaths in construction from highest to lowest is as follows: falls, struck by objects, electrocution, and caught-in/between. these four are collectively known as fatal four.

in the case of falls, the type that is responsible for the overall highest death in the category is falls from roofs.

Answer from: Quest

answer: correct

step-by-step explanation:

What is the slope of the line in the graph? slope is 1 answer=1

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