(#5 cont.) (c) lie between 1.1 and 7.4. 6. (10 points) (a) For the standard norm

Question

(#5 cont.) (c) lie between 1.1 and 7.4. 6. (10 points) (a) For the standard normal distribution, find the 75.17 percentile, (b) For the normal distribution with mean-3 and standard deviation 2.2, find the 75.17 percentile; 7. (Bonus 15 points) Students are to take a pre-course test, there are 35 questions of multiple choices of 4 that is, there are choices of (a), (b), (c) (d)). (a) What is the expected number of correctly answered questions? (b) Use normal approximation to get the approximation of the probability that a student answered 9 questions correctly (round to 4 decimals); (c) Use normal approximation to get the approximation of the probability that a student answered at least 10 questions correctly

Explanation / Answer

a) P(Z < z) = 0.7517

   or, z = 0.68

or, (x - 0)/1 = 0.68

or, x = 0.68

b) P(X < x) = 0.7517

or, P((X - mean)/sd < (x - mean)/sd) = 0.7517

or, P(Z < (x - (-3))/2.2) = 0.7517

or, P(Z < (x + 3)/2.2) = 0.7517

or, (x + 3)/2.2 = 0.68

or, x = 0.68 * 2.2 + 3

or, x = 4.496

7) n = 35

P(correct answer) = 0.25

a) Expected no of correct answer questions = n * p = 35 * 0.25 = 8.75

b) sd = sqrt(n * p * (1 - p)) = sqrt(35 * 0.25 * 0.75) = 2.56

P(X = 9) = P(8.5 < X < 9.5)

              = P((8.5 - mean)/sd < (X - mean)/sd < (9.5 - mean)/sd)

              = P((8.5 - 8.75)/2.56 < Z < (9.5 - 8.75)/2.56)

              = P(-0.10 < Z < 0.29)

              = P(Z < 0.29) - P(Z < -0.10)

              = 0.6141 - 0.4602

               = 0.1539

c) P(X > 10) = P(X > 10.5)

                     = P((X - mean)/sd > (10.5 - mean)/sd)

                     = P(Z > (10.5 - 8.75)/2.56)

                     = P(Z > 0.68)

                     = 1 - P(Z < 0.68)

                     = 1 - 0.7517 = 0.2483

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.