Answer:
Part 1
a) 0.0791
b) 0.000977
c) 0.7627
Part 2
a) 0.049
b) 0.067
c) 0.864 or 0.136 (depending on what the question truly says)
d) 0.806
Step-by-step explanation:
Part 1
Since there are 4 choices per question, and only one correct answer per question.
The probability of getting a question right = (1/4) = 0.25
Probability of getting a question wrong = 1 - 0.25 = 0.75
a) Probability that the first question she gets right is the 5th question means she gets the first 4 questions wrong, and gets the last question.
0.75 × 0.75 × 0.75 × 0.75 × 0.25 = 0.0791
b) Probability that she gets all of the questions right
0.25 × 0.25 × 0.25 × 0.25 × 0.25 = 0.000977
c) Probability that she gets at least one question right = 1 - (probability that she doesn't get any question right) = 1 - (0.75⁵) = 1 - 0.2373 = 0.7627
Part 2
We use standard normal distribution for this
a) Area under (Z< -1.65) = P(z < -1.65) = 1 - P(z ≥ -1.65) = 1 - P(z ≤ 1.65) = 1 - 0.951 = 0.049
b) Area under (Z > 1.5) = P(z > 1.5) = 1 - P(z ≤ 1.5) = 1 - 0.933 = 0.067
c) P(z > -1.1) or P(z < -1.1)
P(z > - 1.1) = 1 - P(z ≤ -1.1) = 1 - 0.136 = 0.864
P(z < - 1.1) = 1 - P(z ≥ - 1.1) = 1 - P(z ≤ 1.1) = 1 - 0.864 = 0.136
d) |Z|>1.3 = P(-1.3 < z < 1.3) = P(z < 1.3) - P(z < -1.3)
P(z < 1.3) = 1 - P(z ≥ 1.3) = 1 - P(z ≤ -1.3) = 1 - 0.097 = 0.903
P(z < -1.3) = 1 - P(z ≥ -1.3) = 1 - P(z ≤ 1.3) = 1 - 0.903 = 0.097
P(z < 1.3) - P(z < -1.3) = 0.903 - 0.097 = 0.806
