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MATH533 � Final Exam Worksheet

Final exam worksheet covering advanced math topics.

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    1 MATH533 – Final Exam Worksheet 1. Given the following sample of 1 0 high temperatures from March: 55, 60, 57, 43, 59, 66, 72, 65, 59, 47. a. Determine the mean.   1 1 1 Mean, 55 60 57 43 59 66 72 65 59 47 10 1 583 10 58.3 n i i x x n                 b. Determine the median.     Arrange the data in ascending order of magnitude, 43, 47, 55, 57, 59, 59, 60, 65, 66, 72 Median Mean of the two middle values Since 10 is even 1 59 59 2 59 n      c. Determine the mode. Mode is the most repeated value in the given series of observations. Here, the value 59 is repeated twice and it is the most repeated value. So the mode is 59. d. Describe the shape of the distribution. Since mean is close to median and mode, the shape of the distribution is approximately symmetric. e. Determine Q1, Q2, Q3 and IQR.

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    2   1 Arrange the data in ascending order of magnitude, 43, 47, 55, 57, 59, 59, 60, 65, 66, 72 Mean of the two middle values in the lower half 1 47 55 2 51 Q           2 3 3 1 , Median Mean of the two middle values Since 10 is even 1 59 59 2 59 Mean of the two middle values in the upper half 1 65 66 2 65.5 IQR 65.5 51 14.5 Q n Q Q Q               2. The contingency table shows classification of students in a Statistics class. From NJ From PA GPA at least 3.0 15 5 20 GPA below 3.0 45 35 80 60 40 100 a. If a student is selected at random, what is the pr obability that he/she is from NJ ? 60 0.6 100  b. If a student is selected at random, what is the probability that he/she has a GPA below 3.0? 80 0.8 100  c. If we know that the student is from PA, what is the probability that he/she has a GPA of at least 3.0?

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    3 5 0.125 40  d. If a student is selected at random, what is the probability that he/she is from NJ and has a GPA below 3.0. 45 0.45 100  e. If a student is selected at random, what is the probability that he/she from PA and has GPA of at least 3.0. 5 0.05 100  3. Your friend is applying for 4 jobs. The hourly pay rate for the 4 jobs are, $8, $12, $15, $20. The probability distribution below shows the probability of getting each of these jobs: Job Pay Rate, X Probability, P(X) 8 .30 12 .20 15 .40 20 .10 a. What is the probability that your friend will get a job paying at least $15/hour?       15 15 20 .40 .10 .50 P X P X P X         b. What is the expected pay rate for your friend?     The expected pay rate, 8 .30 12 .20 15 .40 20 .10 12.8 E X xP x           

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