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.

Write 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

8. You know the minimum, the maximum, and the 25th, 50th, and 75th percentiles

of a distribution. Which of the following measures of central tendency or

variability can you determine?

mean, median, mode, trimean, geometric mean, range, interquartile range,

variance, standard deviation

9. For the numbers 1, 3, 4, 6, and 12:

Find the value (v) for which ?(X-v)2 is minimized.

Find the value (v) for which ?|x-v| is minimized.

10. Your younger brother comes home one day after taking a science test. He says

that some- one at school told him that "60% of the students in the class scored

above the median test grade." What is wrong with this statement? What if he had

said "60% of the students scored below the mean?

Question: 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. a. What is the probability that the freshman is enrolled in both English 105 and Mathematics 101? b. What is the probability that the freshman is enrolled in English 105 but not in Mathematics 101? c. Suppose the freshman chosen is known to be enrolled in Mathematics 101. What is the probability that the freshman is also enrolled in English 105? P(E) = 0.90 P(M) = 0.80 m M P(MnE ) = 0.05 P(EnM') = 0.15 P(MnE) = 0.75Result Pass Fail Total Mathematics 45 35 80 Course English 12 90 Total 93 77 170 2. (3 points) What is the probability that randomly selected student takes a course in Mathematics and fails? 3. (5 points) What is the probability that randomly selected student either takes a course in Mathematics or fails? 4. (7 points) What is the probability that a randomly selected student takes course in Mathematics given the information that student fails?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