Question

1. i) Find the indicated value of Z: 20.00 ii) Find the critical value z* for a cumulative area of 0.025 (a) i) -2.576 (b) (e) i) 2.576 i) 2.576 ii) 1.96 ii) -2.45 ii) - 1.96 (d) i) -2.576 ii) -1.96 2. Let X be a normally distributed random variable X with mean 83 and standard devi- ation 4. Find the critical value x that yields an area of 10% to its right. (a) 88.13 (6) 78.52 (c) 63.10 (d) 85.06 3. At the end of each semester, Professor Mann calculates an overall score for each his students in large sections of Introductory Statistics course. The overall score is cal- culated based on each students performance on homework, attendance, tests, quizzes and a final exam. A final grade is then assigned based on the overall score for the course. In a particular semester, the scores are normally distributed with a mean score of x = 72 and a standard deviation of a = 8. i) Find the probability that a randomly selected student's overall score is more than 80. ii) If the professor decides to give A to the top 18% of the students, what is the minimum score a student can get and still get an A? (a) (b) (c) (d) i) 0.137 i) 0.159 i) 0.121 i) 0.091 ii) 74.8 ii) 79.3 ii) 80.2 ii) 66.8

Answer 1

D j Zoroos = 2:576 - value * for cumulative area As 4 The critical y 0.025 - 196 орном (). al 0.025 XNN (8914) that yields an arear The critical value a - 10 % to it 8 right so zo score for 10% 2 = 11:2816 to its right 80 2 2 = x-4 1 X = utzo - 834 1-2816 X Y = 88013 As option (a) (3) UE 72, 038 a Probability that a randomly selected studente ourall score more than so P( x250) = P1 *-4 > 80-72) - Pizz11 - polka (4) of the professes decide to give a A to to the top 18% of the students, the minimum score a student can get still get A since zo score for the top 18% Z = 0.915 - ge z=x-4 = x= ultzo 5 x = 72 +0.915 X8 1. = 79.3 so Answer (6)