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Q SCI 381 Dr.Bare Name:________________________ Hourly Examination Three Answers 1.a. Use the z-distribution to find the z-values corresponding to the two given x-values. You should find that 82 bushels corresponds to a z-value of -1.75 and 138 bushels corresponds to z = 1.75. From the z-table, the area under the z-curve between these two values = 0.9198. 1.b. Find the z-value with .0500 area to its left in the z-table to be -1.645. Similarly, the z-value with .9500 area to its left is found in the z-table to be 1.645. Using the formula from p. 254 of your text, you transform the z-score to the x-scale and obtain the two x-values of 83.68 and 136.32. 2.a. The max error of estimate is: 4.262. (Here we use the t-table.) 2.b. The 95% C.I. is 120 +(-) 4.262 2.c. We are 95% confident the interval 120 +(-) 4.262 contains the true (unknown) mean blood pressure. 3. Use the definition of the z-variable described in Sec 5.4 and find z = 5.728. From the z-table, the probability that a sample mean is greater than 5.728 standard deviations is about 0. 4.a. Review p. 309 where the finite population correction factor is defined. If n >= 0.05N and sampling is done w/o replacement, then the correction is warranted. Here we have 49 >= 30 so it is needed. 4.b. z-distribution as n>= 30 4.c. E = 1.645 (1.37) = 2.25 and the 90% C.I. = 125 +(-) 2.25 4.d. We are 90% confident that the interval 125 +(-) 2.25 contains the true mean IQ of statistic instructors. 5. Use procedure from p. 332 and chi-square table 6. The appropriate chi-square values from the table are chi-square left = 6.571 and chi-square right = 23.685. The 90% C.I. for the variance is: 21.28 - 76.70 and upon taking the square root, the C.I. for the standard deviation is: 4.61-8.76. 6. Yes, we meet the two conditions for using the normal approximation of the binomial. Both np and nq >= 5. The appropriate z-value calculated using the formula from p. 278 is 1.99. From the z-table, the probability of 30 or more streams containing fish is 1 - .9767 = .0233 7. Use formula from p. 304. n = 43.3 or 44 crows.