MAT 119 8.3 Standard Deviation

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TUTORIAL WITH SOME WORK SHOWN FOR THE FOLLOWING QUESTIONS

  1. The following histograms represent the probability distributions of the random variables X and Y. Determine by inspection which probability distribution has the larger variance.

Figure (a) has the larger variance.

Figure (b) has the larger variance.

The variances are the same.

It is not possible to determine the variance from the histograms.

  1. A study of the records of 85,000 apartment units in a greater metropolitan area revealed the following data.

Year 2002 2003 2004 2005 2006

Average Rent, $ 1348 1339 1317 1304 1355

Find the average of the average rent for the 5 years in question. (Round your answer to the nearest whole number.)

What is the standard deviation for these data? (Round your answer to two decimal places.)

  1. The following table gives the scores of 30 students in a mathematics examination.

Scores 9099 8089 7079 6069 5059

Students 3 7 15 3 2

Find the mean and the standard deviation of the given data. Hint: Assume that all scores lying within a group interval take the middle value of that group. (Round your answers to two decimal places.)

  1. Suppose the following table gives the extra travel time each year, in hours, for peak-period travelers in urban areas with more than 3 million people.

Urban Area Annual Hours of

Delay per Traveler

Los AngelesLong BeachSanta Ana, Ca 65

San FranciscoOakland, CA 53

Atlanta, GA 57

Washington (D.C.VAMD) 62

DallasFort WorthArlington, TX 49

Houston, TX 53

Find the mean of the extra travel time each year, in hours, for peak-period travelers in urban areas with more than 3 million people. (Round your answer to two decimal places.)

What is the standard deviation for these data? (Round your answer to two decimal places.)

  1. The following table gives the percentage of homicide cases in a county ending in pleas or verdicts of guilty from 2004 through 2009.

Year 2004 2005 2006 2007 2008 2009

Conviction Rate (%) 78 91 85 78 82 102

Find the mean of the percentage of homicide cases in the county ending in pleas or verdicts of guilty from 2004 through 2009. (Round your answer to two decimal places.)

of cases

What is the standard deviation for these data? (Round your answer to two decimal places.)

  1. Suppose the number of injuries due to lightning from 1999 through 2008 is given in the following table.

Year 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

Number 248 367 372 255 238 277 309 243 136 211

What is the average number of injuries per year due to lightning in from 1999 through 2008? (Round your answer to two decimal places.)

What is the standard deviation for these data? (Round your answer to two decimal places.)

  1. A probability distribution has a mean of 15 and a standard deviation of 3. Use Chebychev's inequality to find a bound on the probability that an outcome of the experiment lies between the following. (Enter your answers to two decimal places.)

(a) 10 and 20

at least 0.64

(b) 5 and 25

  1. Suppose X is a random variable with mean ? and standard deviation ?. If a large number of trials is observed, at least what percentage of these values is expected to lie between ? ? 3? and ? + 3?? (Round your answer to the nearest whole number.)

at least 89%

  1. A Christmas tree light has an expected life of 210 hr and a standard deviation of 2 hr.

(a) Find a bound on the probability that one of these Christmas tree lights will require replacement between 200 hr and 220 hr. (Enter your answer to two decimal places.)

at least

(b) Suppose a large city uses 190,000 of these Christmas tree lights as part of its Christmas decorations. Estimate the number of lights that are likely to require replacement between 190 hr and 230 hr of use.

  1. Sugar packaged by a certain machine has a mean weight of 5 lb and a standard deviation of 0.03 lb. For what values of c can the manufacturer of the machinery claim that the sugar packaged by this machine has a weight between 5 ? c and 5 + c lb with probability at least 91%?

at least c =

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