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#5396

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5. **A fair coin is flipped 9 times. What is the probability of getting exactly 6 heads?**

11. **A group of students at a school takes a history test. The distribution is normal**

**with a mean of 25, and a standard deviation of 4. (a) Everyone who scores in**

**the top 30% of the distribution gets a certificate. What is the lowest score**

**someone can get and still earn a certificate? (b) The top 5% of the scores get to**

**compete in a statewide history contest. What is the lowest score someone can**

**get and still go onto compete with the rest of the state?**

**12. A person claims to be able to predict the outcome of flipping a coin. This**

**person is correct 16/25 times. Compute the 95% confidence interval on the**

**proportion of times this person can predict coin flips correctly. What**

**conclusion can you draw about this test of his ability to predict the future?**

** **

** **

**Illowsky**

**112. Table 3.22 identifies a group of children by one of four hair colors, and by type of hair.**

**Hair Type Brown Blond Black Red Totals**

** **

**a. Complete the table.**

**b. What is the probability that a randomly selected child will have wavy hair?**

**c. What is the probability that a randomly selected child will have either brown or blond hair?**

**d. What is the probability that a randomly selected child will have wavy brown hair?**

**e. What is the probability that a randomly selected child will have red hair, given that he or she has straight hair?**

**f. If B is the event of a child having brown hair, find the probability of the complement of B.**

**g. In words, what does the complement of B represent?**

**72. You buy a lottery ticket to a lottery that costs $10 per ticket. There are only 100 tickets available to be sold in this lottery. In this lottery there are one $500 prize, two $100 prizes, and four $25 prizes. Find your expected gain or loss.**

**76. Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and**

**a standard deviation of 50 feet.**

**a. If X = distance in feet for a fly ball, then X ~ _____(_____,_____)**

**b. If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than**

**220 feet? Sketch the graph. Scale the horizontal axis X. Shade the region corresponding to the probability. Find ****the probability.**

**c. Find the 80th percentile of the distribution of fly balls. Sketch the graph, and write the probability statement.**

**106. Suppose that a committee is studying whether or not there is waste of time in our judicial system. It is interested in the mean amount of time individuals waste at the courthouse waiting to be called for jury duty. The committee randomly surveyed 81 people who recently served as jurors. The sample mean wait time was eight hours with a sample standard deviation of four hours.**

**a**

** i. x ¯ = __________**

** ii. sx = __________**

** iii. n = __________**

** iv. n – 1 = __________**

**b. Define the random variables X and X ¯ in words.**

**c. Which distribution should you use for this problem? Explain your choice.**

**d. Construct a 95% confidence interval for the population mean time wasted.**

** i. State the confidence interval.**

** ii. Sketch the graph.**

** iii. Calculate the error bound.**** **

**e. Explain in a complete sentence what the confidence interval means.**

** **

** **

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- Posted by: Ace7030
- Subjects: Math Environmental Law
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*Stats Quiz 2 New.docx (37 KB)*

Solution Details:
#5410

Why is a 99% confidence interval wider than a 95% confidence interval?
Solution)
The definition of a confidence interval is that it contains the true population mean. If I have a 95% confidence interval, that means I am 95% certain that the true population mean is in the interval. If I want to be even more certain, I have to widen the interval. If I can be less certain, I can narrow the interval.
So the widest interval will be 99%, and the narrowest would be 90%.
Example:
you're trying to figure out where in the city Comet Donuts is in, but you really don't know for sure. A desperately hungry person hands you a map and asks you to show him where it is. If someone forces you to be 99% accurate, are you going to draw a wide or narrow circle on the map? You can't afford to be wrong - at 99% you're saying that you'll be wrong one time out of 100! So you draw a big circle.
If the person asking doesn't even like donuts, they're just asking for the heck of it, you can be 90% accurate, so you can take a chance and draw a small circle. You'll be wrong 10% of the time.
12. A person claims to be able to predict the outcome of flipping a coin. This person is correct 16/25 times. Compute the 95% confidence interval on the proportion of times this person can predict coin flips correctly. What conclusion can you draw about this test of his ability to predict the future?
Solution)
WE HAVE GIVEN THAT n = 25 and p = 16/25
And we need to construct the 95% C.I. for the proportion of times this person can predict coins flips correctly as,
ṕ± 1.96 * √ (ṕq^/n)
=.64± 1.96 * √ (.64*.36/25)
= .64 ± .1882
So the 95% C.I. is,
(0.4518, 0.8282)
So We Are 95 Out Of 100 Attempts are confident that the values of the samples are lies b/w (.4518,.8282)
15. You take a sample of 22 from a population of test scores, and the mean of your sample is 60.
(a) You know the standard deviation of the population is 10. What is the 99% confidence interval on the population mean?
Solution)
We have given that n = 22, sample mean =60 and σ = 10
The 99% C.I. for the population mean is,
= sample mean ± 2.58 *σ /√n
= 60 ± 2.58 * 10 / √22
= 60 ± 5.501
So, (54.499, 65.501)
(b) Now assume that you do not know the population standard deviation, but the standard deviation in your sample is 10. What is the 99% confidence interval on the mean now?
Solution)
Here we have given that n = 22, ...

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