General Mathematics Statistics

General Mathematics Statistics

Please list step by step solutions, the questions start on page 2.

__1. (5 pts) Which activity could probabilities be computed using a Binomial Distribution?

1. Flipping a coin 100 times

 

1. Throwing a die one hundred times

 

1. Drawing a heart while playing card games

 

1. Activities a and b

 

1. None of the above

 

_____2. (5 pts) Which of the following pairs are NOT independent events?

1. Flipping a coin twice

 

1. Throwing a die twice

 

1. Drawing a heart from a set of poker cards, putting it back, and then drawing another heart.

 

1. Drawing a spade from a set of poker cards, not putting it back and then drawing a diamond

 

1. All of the above are independent events

 

_____3. (5 pts) Given a normal distribution with a mean of 15 and standard deviation of 5, approximately 95% of its area is within:

1. One standard deviation of the mean

 

1. Two standard deviations of the mean

 

1. Three standard deviations of the mean

 

1. Depends on the number of outliers

 

1. Must determine the z-scores first to determine the area

_____4. (5 pts) You had no chance to study for the final exam and had to guess for each question. The instructor gave you three choices for the final exam:

I: 6 questions, each question has 4 choices, must answer at least 5 correct to pass

II: 5 questions, each question has 5 choices, must answer at least 4 correct to pass

III: 4 questions, each question has 10 choices, must answer at least 3 correct to pass

Which final exam format offers the highest probability to pass?

1. Final exam I

 

1. Final exam II

 

1. Final exam III

 

1. All three final formats have equal probabilities

 

1. Need more information to compute probabilities

 

_____5. (5 pts) Consider a normal distribution with a mean of 24 and variance of 9. Approximately 95% of the area lies between which values?

1. 15 and 33

 

1. 21 and 27

 

1. 18 and 30

 

1. 6 and 42

 

1. None of the above

 

_____6. (5 pts) For a standard normal distribution, what’s the probability of getting a positive number?

1. 100%

 

99. 99.7%

 

1. 95%

 

1. 68%

 

1. 50%

_____7. (5 pts) Which description of normal distributions is correct (select all that apply)?

1. You can use the normal distribution to approximate the binomial distribution

 

1. Normal distributions can differ in their means, but their standard deviations must be the same.

 

1. Standard normal distributions cannot differ in both their means and their standard deviations.

 

1. Normal distributions cannot differ in their means, but can differ in their standard deviations.

 

1. None of the above are correct

 

_____8. (5 pts) Consider an extremely right skewed distribution with a mean of 20 and standard deviation of 6. 95% of its area is within:

1. One standard deviation of the mean

 

1. Two standard deviations of the mean

 

1. Three standard deviations of the mean

 

2. 2.5 standard deviations of the mean

 

1. Can’t determine from the information given.

 

_____9. (5 pts) A delivery truck must make stops in eight different cities, designated by the first letter in the name of the city: A, B, C, D, E, F, G, and H. If the order in which the truck visits the eight locations is chosen randomly, what is the probability that the truck will visit them in alphabetical order?

_____10. (5 pts) Acme Airlines flies airplanes that seat 12 passengers. From experience, they have determined, on average, 80% of the passengers holding reservations for a particular flight actually show up for the flight. If they book 13 passengers for a flight, what is the probability (rounded to two decimals) that 12 or fewer passengers holding reservations will actually show up for the flight?

1. 0.85
2. 0.90
3. 0.95
4. 0.99

 

_____11. (5 pts) A jar contains 12 marbles, 5 of which are blue and 7 of which are red. If 4 marbles are chosen at random and without replacement, what is the probability of selecting 3 blue marbles and 1 red marble?

1. b. c. d. 5 3 7 1 12 4 C CC 5 3 7 1 12 4 P PP 5 2 7 2 12 C P  5 3 7 1 12 C P 

_____12. (5 pts) If events A and B are mutually exclusive events, then which of the following is true:

1. P(A ∩ B) = P(A)

 

1. P(A ∪ B) = P(A) + P(B)

 

1. P(A) – 1 = P(B)

 

1. P(A) = P(B)

 

__13. (5 pts) If events A and B are complementary events, each with non-zero probability, then:

 

1. and are mutually exclusive A B
2. A and B are independent
3. Both (a) and (b) are true
4. Neither (a) nor (b) are true

 

_____14. (5 pts) A recent study stated students earn an average of $4500 during their summer break. A random sample of students had a sample mean of $3975 earned. The associated 95% confidence interval was $3525 < μ < $4425. This confidence interval is interpreted as:

1. If we were to repeat our sampling many times, then about 95% of all the confidence intervals will contain a value of about $4500

 

1. About 95% of the sample students have an average summer earnings that is not $4500 as the government claims

 

1. If we repeat our sampling many times, then about 95% of our confidence intervals will contain the true average earnings of students during their summer break

 

1. Because our specific confidence interval does not contain the value $4500 there is a 95% probability that the true average summer earning is not $4500

 

15. (10 pts) An engineering company claims to have produced a longer lasting D battery with an average life span of 16.2 hours with a standard deviation of 0.75 hours. An independent testing firm randomly selected 30 of these new D batteries and found the sample mean life span was 15.9 hours. What is the probability of getting a random sample of 30 batteries in which the sample mean life span is 15.9 hours or less? Based on this probability, is the engineering company’s claim reasonable (be sure to state why and show your work)? Round your probability to THREE decimal places.
16. (10 pts) A company has initiated a training program for new hires. After surveying 16 new employees, they determined the average training time was 7 hours with a sample standard deviation of 2 hours. Assume that the underlying population is normally distributed. Show your work and round your CI to THREE decimal places.
17. Define the random variable X for this problem in words.

 

1. Define the random variable 𝑋̅ in words.

 

1. Construct a 90% confidence interval for the population mean length of time of new hire training.

 

1. Why does the error bound change if the confidence level is increased to 95%?

 

1. Which interval is more precise, 90% or 95% (and state why)?

STAT 200 (6361) QUIZ 2 February 2016 Instructor: S. Oimoen8STUaertrtrrrDENT NAME/14 OL1STUDENT NAME

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17. (10 pts) A researcher randomly surveyed 400 high school students and determined 335 stated they have a mobile phone. We are interested in the population proportion of students who have mobile phones.
18. Define the random variable X for this problem in words.

 

1. Define the random variable P’ in words.

 

1. Construct a 99% confidence interval for the population proportion of high school students who claim to have a mobile phone. Round your CI to THREE decimal places.

 

1. Calculate the error bound.