Class:STASTISTICSin Psychology

ANSWER BOTH PARTS I & II.

(SHOW AS MUCH WORK AS POSSIBLE)

Part I: Calculating z-scores

Assume that 13 high school students at Pierre check their social media accounts the following number of times each day.

7, 6, 5, 8, 9, 9, 3, 7, 6, 5, 8, 9, 9

1. Compute the mean and standard deviation (population form) for this set of data where N = 13
2. Compute the z-scores for each of the 13 raw scores (note that some of the raw scores are the same so you only need to compute the z for those repeated raw scores once) (SHOW AS MUCH WORK AS POSSIBLE)

---------------------------------------------------------------------

Part II: Using z-scores to calculate proportions, percentages and probabilities using the normal distribution

Now assume that the entire population of Pierrehigh school students check their social media accounts on average 7 times a day with a standard deviation of 2.5 (yes, the average and standard deviation for the population are different than the sample of 13 students you just calculated). Further assume that the population is normally distributed. Answer the following questions using a mean of 7 and a SD of 2.5.

1. What proportion of the population of students check their accounts more than 5 times a day? (Hint: first you have to convert the 5 to its z score and then use the z-table to answer the question)
2. What proportion of the population of students check their accounts more than 8.5 times a day? (Hint: first you have to convert the 8.5 to its z score and then use the z-table)
3. What proportion of the population of students check their accounts between 6 and 8 times a day? (Hint: first you have to convert both 6 and 8 to z-scores and then use the z table)
4. What is the percentile rank of a student in the population who checks their account 5 times a day? (Hint: first you have to convert the 5 to its z score and then use the z table)
5. How many times a day would a person in the population check their account if they were at the 75th percentile? (Hint: first you have to go to the z-table to find the z score knowing that 75% of the scores fall below it, then you can use the z-score to find the original raw score X value)

(SHOW AS MUCH WORK AS POSSIBLE)