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[AP Statistics] 6.1b Continuous Random Variables

Last updated 5 months ago
12 questions
Previously, we learned about Discrete Random Variables, which can take on specific values.

Example:

Y = the height of a randomly chosen woman

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Sometimes, a continuous random variable can be described using a normal density curve

Problem: The heights of young women can be modeled by a Normal distribution
with mean µ = 64 inches and standard deviation σ = 2.7 inches. Suppose we choose a young woman at random and let Y = her height (in inches).



Find P(68 ≤ Y ≤ 70). Round to two decimal places.

Interpretation of probabilities:

The probability that a randomly selected young woman has a height between 68 and 70 inches is about (answer above).
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Continuous Random Variables can also be modeled by uniform density curves (horizontal line)

Problem: Selena works at a bookstore in the Denver International Airport. She takes the airport train from the main terminal to get to work each day. The airport just opened a new walkway that would allow Selena to get from the main terminal to the bookstore in 4 minutes. She wonders if it will be faster to walk or take the train to work.

Let Y = Selena’s journey time to work (in minutes) by train on a randomly selected day.

The probability distribution of Y can be modeled by a uniform density curve on the interval from 2 to 5 minutes.



What should the height of this density curve be? Answer as a fraction

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Find the probability that it will be quicker for Selena to take the train than to walk that day.

Answer as a fraction

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Round to two decimal places.

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Find the value of P(-1<Y<1). Round to two decimal places.

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Interpret the value you found above

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What is the Expected Value of Y?

Hint: This is the same as the mean.

Round to two decimal places.

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(May require some casual Geometry)

Round to two decimal places.

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Round to two decimal places.

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Find the probability that the pregnancy lasts between 325 and 345 days. Round to two decimal places.

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Write the probability you found above with probability notation.

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Find the 80th percentile of the distribution (invNorm may be helpful). Round to two decimal places.