10. A population of raw scores is normally distributed with =60 and o=14. Determine the z scores for the following raw scores taken from that population:

a. 76

b. 48

f. 46

11. For the following z scores, determine the percentage of scores that lie beyond z:

a. 0 b. 1

c. 1.54

f. -0.45

12. For the following z scores, determine the percentage of scores that lie between the mean and the z score:

a. 1

b. -1 c. 2.34

e. 0

f. 0.68

g. -0.73

13. For each of the following, determine the z score that divides the distribution such that the given percentage of scores lies above the z score (round to two decimal places):

d. 30%

e. 80%

15. At t he end of a particular quarter, Carol took four final exams. The mean a nd standard deviation for each exam along with Carol's grade on each exam are listed here. Assume that the grades on each exam are normally distributed.

Exam Mean Standard Deviation Carol's Grade French

75.4 6.3 78.2 History 85.6 4.1 83.4 Psychology 88.2 3.5 89.2 Statistics 70.4 8.6 82.5

a. On which exam did Carol do best, relative to the other students taking the exam?

b. What was her percentile rank on t his exam?

16.A hospital in a large city records the weight of every infant born at the hospital. The distribution of weights is normally shaped, with a mean = 2.9 kilograms and a standard deviation 0 .45. Determine the following:

a. The percentage of infants who weighed less than 2.1 kilograms

b. The percentile rank of a weight of 4.2 kilograms

c. The percentage of infants who weighed between 1.8 and 4.0 kilograms

d. The percentage of infants who weighed between 3.4 and 4.1 kilograms

e. The weight that divides the distribution such that 1% of the weights are above it

f. Beyond what weights do the most extreme 5% of the scores lie?

g. If 15,000 infants have been born at the hospital, how many weighed less than 3.5 kilograms?

17. A statistician studied t he re cords of monthly rainfall for a pa rticular geographic locale. She found that the average monthly rainfall was normally distributed with a mean 8.2 centimeters and a standard deviation 2.4. What is the percentile rank of the following scores?

b. 14.3

d. 4.1

18. Using the same population parameters as in Problem 17, find what percentage of scores are above the following scores:

b. 13.8

c. 7.6

19. Using t he same population parameters a s i n Problem 17, i nd what percentage of scores are between the following scores:

a. 6.8 and 10.2

b. 5.4 and 8.0

c. 8.8 and 10.5

24. A psychologist interested in the intelligence of children develops a standardized test for selecting "gifted" children. The test scores are normally distributed, with n=75 and o= 8. Assume a gifted child is defined as one who scores in the upper 1% of the distribution. What is the minimum score needed to be selected as gifted?

Please write down the formula, then put the numbers in the formula (at a MINIMUM) before giving your answer.

e.g. What percentage of people have an IQ above 120 if the mean = 100 and the st dev = 16? Please note that we will be lenient about proper symbols due to the problems typing formulas. this is what is considered a finished answer

Z = (X-u)/o = (120-100)/16 = 20/16 = 1.25 area (col C) = .1056

Therefore, 10.56 % of people have an IQ above 120.

1a) . You work as a statistician for a large national car manufacturer. You have just finished analyzing the data for how long it took 235 assemble line teams to install a transmission. The average number of minutes required to install a transmission was 12 minutes (st dev = 0.4).How many teams took more than 12.6 minutes to install a transmission?

1b) Using the data from question 1a) what proportion of teams took more than 11.7 minutes?

1c). You check the statistics for the National Hockey League (NHL) and write down the average (mean) number of minutes each player spends on the ice as well as the standard deviation. You note that your favourite player's time on the ice was 24 minutes and calculate this is 1.2 standard deviations above the mean. A friend asks you what the mean was but you cannot remember, but you do recall that the standard deviation was 3.7. What is the mean number of minutes played by hockey players in the NHL?

1d. If the grades on a test has an average of 68 (SD = 12.5) how many standard deviations above the mean would you have to be if you wanted to be in the top 20% of your class?

What actual mark would need to be in the top 20% of the class?

2. You wonder if there is a difference in support for a universal basic income based on political outlook. You have access to a data set of 700 people who work at Brock University. From this group 350 people describe themselves as "liberal thinking" and 350 people who describe themselves as "conservative thinking".You select 30 people who describe themselves as "liberal" and 30 who describe themselves as "conservative" and ask them to rate how much they support the idea of a universal basic income on a scale of 0-100

a) what is the population?

b) what is(are) the sample(s)?

c) what is the IV?

d) what is the DV?

e) what type of measurement scale is the DV?

f) Is this an experiment or a study (and why)?