88. Individual Stock Price An individual stock is selected at ...

Question

88. Individual Stock Price An individual stock is selected at random from the portfolio represented by the box-and-whisker plot shown. Find the probability that the stock price is between $21 and $50.

Accepted Answer

Hello there. Today we're gonna solve the following practice problem together. So, first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A random item is selected from a shipment of packaged cereals. The shipment's price distribution in dollars is summarized in the box and whisker plot below. What is the probability that the price of the selected cereal box is between 10 and $18? Awesome. So it appears for this particular problem we're trying to determine ultimately what the probability is that the price of the selected cereal box is between 10 and $18. Awesome. So, once again, now that we know what we're ultimately trying to solve, we're ultimately trying to figure out the probability that the price of the randomly selected cereal box from this shipment is between $10.18 dollars. So looking at our box and whisker plot, which is represented in blue, you can see that our vertical axis denotes the price distribution in units of dollars, and we will, we will go into depth about this box and whisker plot in just a second. So, before we do that, let's quickly read off our multiple choice answers to see what our final answer might be. So A is 0.50, B is 0.35, C is 0.05, and D is 0.15. Awesome. So, first off, in order to solve this particular problem, we need to recall and understand, we need to recall how to understand and interpret a box and whisker plot. So, as we should recall a note, a box and whisker plot divides the data into 4 quartiles, each representing 25% of the data. And the key components are the minimum, which is the smallest data point or the lower whisker. The first quartile, Q1, is the 25th percentile, which is the lower edge of the box. The median, which is Q2, is the 50th percentile, which is the middle line of the box. And our third port tile, Q3, is the 75% percentile, which is the upper edge of our box. And then finally we have the maximum, which is the largest data point or the upper whisker. So now our step two is we need to extract the values from our plot. So looking at our box and whisker plot, we know that the minimum is equal to $6 as we could see, because that is our lower whisker, which I'll highlight in yellow. We also know the first quartile Q1 and Q1. is equal to $10 as we could see because once again, the first quartile is the lower edge of our box. Awesome. And then we have our median Q2 and Q2 is gonna be equal to $14 because that's the middle point of our box. And then our third quartile, Q3, and Q3 is equal to $18 and that is the upper point of our box, and then finally, the upper whisker, which is our maximum value, is going to be equal to, as you can see from our box and whisker pot, it's gonna be equal to $22. Fantastic. So now, Our third step is we need to identify the range of interest, so we're interested from $10 to $18. So once again we're our range is $10 to $18. So this spans from Q1 to Q3. So with that in mind, our 4th and final step is we need to calculate the probability. So as we should recall a note, the range from Q1 to Q3 covers the middle 50% of the data from the 25th percentile to the 75th percentile. So therefore, without a doubt, the probability that a randomly selected cereal box has a price between $10.18 dollars is 50% or 0.50, and that is our final answer. Hooray, we did it. So therefore, without a doubt, our final answer has to be multiple choice answer letter A, which once again is 0.50. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

88. Individual Stock Price An individual stock is selected at random from the portfolio represented by the box-and-whisker plot shown. Find the probability that the stock price is between $21 and $50.

Key Concepts

Box-and-Whisker Plot

Probability

Interquartile Range (IQR)

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