An alrline knows from experience that the distribution of the number of suitcases that get lost each week on a certaln route Is approximately nor u=17.4 and o=3.4. What is the probability that during a given week the airline will lose less than 20 suitcases? 00.7778 O0.2778 O 0.2222
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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**Probability and Statistics in Real-Life Applications**
An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with a mean (μ) of 17.4 and a standard deviation (σ) of 3.4. What is the probability that during a given week the airline will lose less than 20 suitcases?
- **0.7778**
- 0.2778
- 0.2222
- 0.7222
[**Diagram Explanation:**
There is no diagram or graph provided in the image; the content is entirely text-based with a single-selection answer choice format.]
For this problem, students need to use the properties of the normal distribution to determine the probability. This involves finding the Z-score for the value of 20 suitcases and then using Z-tables or statistical software/tools to find the corresponding probability.
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**Calculating the Z-score:**
\[ Z = \frac{(X - \mu)}{\sigma} \]
\[ Z = \frac{(20 - 17.4)}{3.4} \]
\[ Z = \frac{2.6}{3.4} \]
\[ Z ≈ 0.7647 \]
Using a Z-table or normal distribution calculator, find the probability corresponding to a Z-score of 0.7647.
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Continue Answering to practice your knowledge of Z-scores and probability in normal distributions.
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