What are the mean and standard deviation of the standard normal distribution?

(b) What would be the mean and standard deviation of a distribution created by

multiplying the standard normal distribution by 8 and then adding 75?

3. The normal distribution is defined by two parameters. What are they?

4. What proportion of a normal distribution is within one standard deviation of the

mean? (b) What proportion is more than 2.0 standard deviations from the mean?

(c) What proportion is between 1.25 and 2.1 standard deviations above the mean?

5. A test is normally distributed with a mean of 70 and a standard deviation of 8.

(a) What score would be needed to be in the 85th percentile? (b) What score

would be needed to be in the 22nd percentile?

6. Assume a normal distribution with a mean of 70 and a standard deviation of 12.

What limits would include the middle 65% of the cases?

7. A normal distribution has a mean of 20 and a standard deviation of 4. Find the Z

scores for the following numbers: (a) 28 (b) 18 (c) 10 (d) 23

8. Assume the speed of vehicles along a stretch of I-10 has an approximately

normal distribution with a mean of 71 mph and a standard deviation of 8 mph.

a. The current speed limit is 65 mph. What is the proportion of vehicles less than

or equal to the speed limit?

b. What proportion of the vehicles would be going less than 50 mph?

267c. A new speed limit will be initiated such that approximately 10% of vehicles

will be over the speed limit. What is the new speed limit based on this criterion?

d. In what way do you think the actual distribution of speeds differs from a

normal distribution?

9. A variable is normally distributed with a mean of 120 and a standard deviation

of 5. One score is randomly sampled. What is the probability it is above 127?

10. You want to use the normal distribution to approximate the binomial

distribution. Explain what you need to do to find the probability of obtaining

exactly 7 heads out of 12 flips.

11. A group of students at a school takes a history test. The distribution is normal

with a mean of 25, and a standard deviation of 4. (a) Everyone who scores in

the top 30% of the distribution gets a certificate. What is the lowest score

someone can get and still earn a certificate? (b) The top 5% of the scores get to

compete in a statewide history contest. What is the lowest score someone can

get and still go onto compete with the rest of the state?

12. Use the normal distribution to approximate the binomial distribution and find

the probability of getting 15 to 18 heads out of 25 flips. Compare this to what

you get when you calculate the probability using the binomial distribution. out to four decimal places.

13. True/false: For any normal distribution, the mean, median, and mode will be

equal.

14. True/false: In a normal distribution, 11.5% of scores are greater than Z = 1.2.

15. True/false: The percentile rank for the mean is 50% for any normal distribution.

16. True/false: The larger the n, the better the normal distribution approximates the

binomial distribution.

17. True/false: A Z-score represents the number of standard deviations above or

below the mean

Suppose you take 50 measurements on the speed of cars on Interstate 5, and

that these measurements follow roughly a Normal distribution. Do you expect

the standard deviation of these 50 measurements to be about 1 mph, 5 mph, 10

mph, or 20 mph? Explain.

28. Suppose that combined verbal and math SAT scores follow a normal

distribution with mean 896 and standard deviation 174. Suppose further that

Peter finds out that he scored in the top 3% of SAT scores. Determine how high

Peter's score must have been.

29. Heights of adult women in the United States are normally distributed with a

population mean of ?= 63.5 inches and a population standard deviation of ? =

2.5. A medical re- searcher is planning to select a large random sample of adult

women to participate in a future study. What is the standard value, or z-value,

for an adult woman who has a height of 68.5 inches?

30. An automobile manufacturer introduces a new model that averages 27 miles

per gallon in the city. A person who plans to purchase one of these new cars

wrote the manufacturer for the details of the tests, and found out that the

standard deviation is 3 miles per gallon. Assume that in-city mileage is

approximately normally distributed.

a. What is the probability that the person will purchase a car that averages less

than 20 miles per gallon for in-city driving?

b. What is the probability that the person will purchase a car that averages

between 25 and 29 miles per gallon for in-city driving

??

1. I love sweets! In my sweet research, I have found. The probability that a randomly selected person likes cakes is 7. The probability that a randomly selected person likes chocolate chip cookies is 6. The probability that a randomly selected person likes either cakes or cookies is 85. Let the event: 0 -3 A = Event that a randomly selected person likes cakes. D.6 B - Event that a randomly selected person likes cookies. Given the information above answer the following questions, (a) (5 points) Draw a Venn Diagram and update as you complete the quiz. (b) (4 points) What is the probability that the selected person likes both cakes and cookis Write out the probability in mathematical symbols as well as calculate probability. ( PUB ) = PCA) + PCG ) - P ( AnB ) = 10.7+ 0.6 - 0.35 20.45 (c) (4 points) What is the probability that the person likes cakes, but not cookies? Write the probability in mathematical symbols as well as calculate probability. (d) (4 points) What is the probability that the person likes cakes only or cookies only? out the probability in mathematical symbols as well as calculate probability. (e) (4 points) What is the probability that they do not like either cakes or cookies? Wri the probability in mathematical symbols as well as calculate probability. 2. (4 pts) Consider the following..Suppose you toss a fair coin five times, which of the fo events (if any) is least likely to occur and EXPLAIN why? (a) HHHHH - the event heads on all flips (b) HTHTH - the event heads on the first flip, tails on the second flip, etc... (c) HHHTT - the event with heads on the first 3 flips and tails on the last two flips e Helpful Propositions: lements: P(A') = 1 - P(A) two events, A and B. P(AUB) = P(A) + P(B) - P(An B)Question (1) In a high school graduating class of 100 students, 54 studied mathematics, 69 studied history, and 35 studied both mathematics and history. If one of these students is selected at random, find the probability that (a) the student take mathematics or history; (b) the student take history but not mathematics; (c) the student does not take history if he took mathematics. Solution:7 Exercise 7 In a certain college, 25% of the students failed mathematics, 15% failed chemistry and 10% failed both mathematics and chemistry. A student is selected at random. a) Dene the two relevant events. b) If the student failed chemistry, what is the probability that he failed mathematics? (3) If the student failed mathematics, what is the probability that he failed chemistry? (1) What is the probability that the student failed mathematics or chemistry e) What is the probability that the student failed neither mathematics nor chemistry? 0.05 QUESTION 11 1.00000 points At a liberal arts college, 90% of the freshmen are enrolled in English 105, 80% are enrolled in Mathematics 101 and 5% are enrolled in Mathematics 101 but not in English 105. A freshman is randomly selected. What is the probability that the freshman is enrolled in English 105 but not in Mathematics 101? noljesup 0.90 O 0.80 O 0.75 0.15 0.05