Question

1.)  A student takes a ten-question true-false quiz, but did not study and randomly guesses each answer. Find the probability that the student passes the quiz with a grade of at least 70% of the questions correct.

1. Identify
2. First, find the number of correct questions needed to get 70%.
3. Then write an appropriate probability statement.
4. Then find the probability

2.)  Suppose that about 85% of graduating students attend their graduation. A group of 22 graduating students is randomly chosen.

1. In words, define the random variable X.
2. List the values that X may take on.
3. Give the distribution of X. X ~ _____(_____,_____)
4. How many are expected to attend their graduation?
5. Find the probability that 17 or 18 attend.
6. Based on numerical values, would you be surprised if all 22 attended graduation? Justify your answer numerically.

Answer 1

Answer 1)

Getting at least 7 questions right means getting 7,8,9 or 10 questions right.

Probability of getting any question right or wrong = 1/2

So, the probability of getting 7 questions right =

(number of ways of choosing 7 questions)* (probability of getting 7 correct answers)*(probability of getting 3 incorrect answers)

= (10C7)*((1/2)^10)=0.117185

Similarly, the probability of getting 8 questions right = (10C8)*((1/2)^10)=0.04394

Probability of getting 9 questions right = (10C9)*((1/2)^10)=0.00976

Probability of getting 10 questions correct = (1/2)^10=0.00097

Therefore the probability of getting atleast 7 correct answers = 0.117185+0.04394+0.00976+0.00097 = 0.172 (Ans)

Answer 2 )

In summary, the answers are as follows:-

X is the number of graduating students attending the graduation

X = 0,1,2,.....,21,22

E(x) = n*p = 18.7

P(x=17 or 18) = 0.32487

P(x=22) = 0.028

Yes, I will be suprised if all 22 students attend their graduation, since the probabilty is very low.