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Pavlova-9 [17]
3 years ago
13

A survey of magazine subscribers shows that 19% rented a car during the past twelve months for business reasons, 52% rented a ca

r during the last twelve months for personal reasons, and 3% rented a car during the last twelve months for both business and personal reasons.
a. What is the probability that a subscriber rented a car during the past 12 months for
business or personal reasons?
b. What is the probability that a subscriber did not rent a car during the past 12 months
for either business or personal reasons?
Mathematics
1 answer:
irinina [24]3 years ago
4 0

Answer:

a. 0.68 or 68%

b. 0.32 or 32%

Step-by-step explanation:

a. The probability that a subscriber rented a car during the past 12 months for  business or personal reasons (P(R)) is given by the probability that they rented a car for business reasons (P(B)=0.19), added to the probability that they rented for personal reasons (P(P)=0.52), subtracted by the probability that they rented for both reasons (P(B and P) = 0.03):

P(R)=P(B)+P(P)-P(B\cap P)\\P(R) = 0.19+0.52-0.03\\P(R)=0.68

b. The probability that a subscriber did not rent a car during the past 12 months  for either business or personal reasons (P(N)) is 100% minus the probability that they rented a car (P(R) = 0.68).

P(N) = 1-P(R) = 1-0.68\\P(N) =0.32

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Answer:

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\sum_{i=1}^n y_i =1227

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With these we can find the sums:

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=24059-\frac{459^2}{9}=650

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Step-by-step explanation:

For this case we assume the following dataset given:

x: 38,41,45,48,51,53,57,61,65

y: 116,120,123,131,142,145,148,150,152

For this case we need to calculate the slope with the following formula:

m=\frac{S_{xy}}{S_{xx}}

Where:

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}

So we can find the sums like this:

\sum_{i=1}^n x_i =459

\sum_{i=1}^n y_i =1227

\sum_{i=1}^n x^2_i =24059

\sum_{i=1}^n y^2_i =168843

\sum_{i=1}^n x_i y_i =63544

With these we can find the sums:

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=24059-\frac{459^2}{9}=650

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=63544-\frac{459*1227}{9}=967

And the slope would be:

m=\frac{967}{650}=1.488

Nowe we can find the means for x and y like this:

\bar x= \frac{\sum x_i}{n}=\frac{459}{9}=51

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And we can find the intercept using this:

b=\bar y -m \bar x=136.33-(1.488*51)=60.442

So the line would be given by:

y=1.488 x +60.442

And then the best predicted value of y for x = 41 is:

y=1.488*41 +60.442 =121.45

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