Question

Binomial probability:

1. Jasmine is taking a 20 question test for her driver's permit. Each question has 4 choices and she guesses on each question (since she never studied her manual!). What is the probability that she gets exactly 16 questions correct?

2. Mr. Evans is a great EMT technician. He is able to save his patients 98% of the time. If
he has 12 patients, what is the probability that exactly 2 are not saved?

3. The baker is able to make a perfect pastry 97% of the time. If he bakes 75 pies, what is
the probability that exactly 45 turn out?

4.  Suppose that Trey is a basketball player who normally makes 80% of his free throws. Assume that he takes 6 free throw shots Tuesday night. What is the probability that he makes exactly 5 of his shots?

5. Page County Insurance Company records indicate that 12% of all teenage drivers have been ticketed for speeding. Of the 143 teenagers that graduated, what is the probability that exactly 23 of them have been ticketed for speeding?

6. Pepsi is running a sales promotion in which 3% of all bottles have a "FREE" logo under
the cap. What is the probability that you find exactly two free logos in a 12-pack?

Normal distribution:

7. The distribution of annual profit at the chain of Shoe Palace stores was approximately normal with a mean of $457,300 and a standard deviation of $58,000. The CEO of the company would like to reassess the efficiency of all managers of the stores with the lowest 15% of profits. What is the maximum annual profit at the stores that fit in the lowest 15%?

8. If the population of monthly internet bills for the Ida neighborhood has a mean of $82.00 and a standard deviation of $7.50, what is the probability of selecting a household at random whose monthly bill is $64.00 or less?

9. The administration is planning on giving assessments to the top 10% of seniors. If the mean of the senior class GPAs is 3.38 with a standard deviation of 0.15, what is the indicated z-score?

10. Indicate whether the following statistics can be examples of binomial probability distributions:

a.) results of spinning a 4-color spinner

b.) results of flipping a quarter

c.) results of drawing a red or black suit from a deck of cards

d.) results of hitting red light or green light at the intersection of Main and Rt. 340

Answer 1

Pdf of a Binomial distribution is given as:

P(X=x) : nCx*(p)^x*(1-p)^n-x

Where n= total number in the sample

p= Probability of success

x= number of successes

1. Here n= 20, p= 1/4 (since she guesses each question Probability of each being correct is 1/4)

We want, P(X=16) = 20C16*(1/4)^16*(3/4)^4 <0.000001

2. Here n= 12, p=0.98, we want 2 to not be recovered, so 10 should recover.

So, P(X=10) = 12C10*0.98^10*0.02^2 = 0.0216

3. Here n= 75, p= 0.97, we want exactly 45 perfect pastries.

So P(X=45) = 75C45*0.97^45*0.03^30 <0.000001

4. Here n=6, p=0.8 ,

We want, P(X=5) = 6C5*0.8^5*0.2 = 0.39322