2.21 and 2.22 please? A set of n = 10 measurements consists of die values 5, 2,
ID: 2961316 • Letter: 2
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2.21 and 2.22 please?
A set of n = 10 measurements consists of die values 5, 2, 3, 6, 1, 2, 4, 5, 1, 3. Use the range approximation to estimate the value of s for this set. (HINT: Use the table at the end of Section 2.5.) Use your calculator to lind the actual value of s. Is the actual value close to your estimate in part a? Draw a dotplol of this data set. Are the data mound-shaped? Can you use Tchebysheff's Theorem to describe this data set? Why or why not? Can you use the Empirical Rule to describe this data set? Why or why not? Suppose you want to create a mental picture of the relative frequency histogram for a large data set consisting of 1000 observations, and you know that the mean and standard deviation of the data set are 36 and 3, respectively. If you are fairly certain that the relative frequency distribution of the data is mound-shaped, how might you picture the relative frequency distribution? (HINT: Use the Empirical Rule.) If you have no prior information concerning the shape of the relative frequency distribution, what can you say about the relative frequency histogram? (HINT: Construct intervals x- plusminus ks for several choices of k.) A distribution of measurements is relatively mound-shaped with mean 50 and standard deviation 10. What proportion of the measurements will fall between 40 and 60? What proportion of the measurements will fall between 30 and 70? What proportion of the measurements will fall between 30 and 60? If a measurement is chosen at random from this distribution, what is the probability that it will be greater than 60? A set of data has a mean of 75 and a standard deviation of 5. You know nothing else about the size of the data set or the shape of the data distribution. What can you say about the proportion of measurements that fall between 60 and 90? What can you say about the proportion of measurements that fall between 65 and 85? What can you say about the proportion of measurements that are less than 65? Driving Emergencies The length of time quired for an automobile driver lo respond lo a particular emergency situation was recorded for n = 10 drivers. The limes (in seconds) were .5, .8, 1.1, .7.9, .7, .8, .7, .8. Scan the data and use the procedure in Section to find an approximate value for s. Use this value check your calculations in part b. Calculate the sample mean x- and the standard deviation s. Compare with part a. Packaging Hamburger Meat This listed here are the weights (in pounds) of 27 packages of ground beef in a supermarket mean display: 1.08 .99 .97 1.18 1.41 1.28 .83 1.06 1.14 1.38 .75 .96 1.08 .87 .89 .89 .96 1.12 1.12 .93 1.24 .89 .98 1.14 .92 1.18 1.17 Construct a stem and leaf plot or a relative frequency histogram to display the distribution weights. Is the distribution relatively mound-shaped? Kind the mean and standard deviation of the data set. Find the percentage of measurements in the intervals x- plusminus s, x- plusminus 2s, and x- ± 3s. How do the percentages obtained in part c come with those given by the Empirical Rule? Explain How many of the packages weigh exactly 1 pc Can you think of any explanation for this? Breathing Rates Is your breathing rate normal? Actually, there is no standard breathing rate humans. It can vary from as low as 4 breaths per minute to as high as 70 or 75 for a person engagement strenuous exercise. Suppose that the resting breathing rates for college-age students have a relative frequency distribution that is mound-shaped, with a mean ec 12 and a standard deviation of 2.3 breaths per minute.Explanation / Answer
2.21
a) prob = 2 * 0.84134 - 1
= 0.68268
b) prob = 2*0.97725 - 1
= 0.9545
c) prob = 0.84134 - 1 + 0.97725
=0.81859
d) prob = 1 - 0.84134
= 0.15866
2.22
a) prob = 2* 0.99865 - 1
= 0.9973
b) prob = 2*0.97725 - 1
= 0.9545
c) prob = 1 - 0.84134
= 0.15866
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