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Masteriza [31]
2 years ago
15

Two different floor plans are being offered in a new housing development. Several prospective buyers from three different age gr

oups were surveyed about which plan they preferred. Find the probability that a randomly selected buyer preferred Plan A or was in the 40- to 49-year-old age group.

Mathematics
1 answer:
zepelin [54]2 years ago
3 0

Answer:

0.677

Step-by-step explanation:Add up the values in the plan A column. There are 10+12+16 = 38 people who prefer plan A.

Add up the values in the "40-49" row to find that 16+8 = 24 people are ages 40 to 49.

We have 38+24-16 = 46 people who either prefer plan A, are aged 40-49, or fit both descriptions. I subtracted off 16 because those 16 people were counted twice when adding 38 and 24.

An alternative way to get this value of 46 is to add up everything that is in column1 or row 3 (or both). So that would get 10+12+16+8 = 46.

Now add up everything in the table to find out how many people were surveyed total. That would be 10+7+12+15+16+8 = 68 people overall.

The probability of someone liking plan A, or being age 40-49, or both is 46/68 = 0.6765 approximately. Rounding to 3 decimal places gives 0.677

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Answer:

36.32% probability that at least 47 people experience flu symptoms. This is not an unlikely event, so this suggests that flu symptoms are not an adverse reaction to the drug.

Step-by-step explanation:

I am going to use the normal approximation to the binomial 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:

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The standard deviation of the binomial distribution is:

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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 = 1164, p = 0.038

So

\mu = E(X) = np = 1164*0.038 = 44.232

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = 6.5231

Estimate the probability that at least 47 people experience flu symptoms.

Using continuity correction, this is P(X \geq 47 - 0.5) = P(X \geq 46.5), which is 1 subtracted by the pvalue of Z when X = 46.5.

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

Z = \frac{46.5 - 44.232}{6.5231}

Z = 0.35

Z = 0.35 has a 0.6368

1 - 0.6368 = 0.3632

36.32% probability that at least 47 people experience flu symptoms. This is not an unlikely event, so this suggests that flu symptoms are not an adverse reaction to the drug.

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