Question

(Multiple part question) The following normal curve represents scores from a population on a test of musical ability. The population mean of the test is µ=60. The population standard deviation of the test is σ=14.

a. What proportion (not percentage) of people have scores above 69 (rounded to four decimals) given that a z score for 69 = 0.64?

b. What proportion (not percentage) of people have scores below 43 (rounded to four decimals) given that a z score for 43 = -1.21?

c. What percentage (not proportion) of people have scores above 48 (rounded to two decimals) given that a z score for 48 = -0.86?

d. What score (rounded to two decimals) cuts off the bottom 5% of the scores?

e. What is the percentile rank (rounded to whole number) of someone who scores a 71? (write only the number not the "th" or "st" - for example, if it's 1st percentile, just write 1 - if it's 50th, only write 50)

f. What are the two scores (rounded to two decimals) that cut off the middle 25% of cases? Explain your work - what z-scores did you use? What did you do with them to get the scores?

g. What proportion (not percentage) of people have scores between 55 and 75? Round to four decimals

Answer 1

Given that-. A= 60 , 8:14 o find 14 P/Z > 0.64) 1-o-8869 = IP(XA43) = 0-1131 PX48) 0-805I lay Tognd, 2 such that PC><%) = o-05 find. 2-score such that 05 i na でtabl 'e ωeget z-score corespond arr Probability oos is 1-645 645 (14) 60 2-23-03 t 60 56-37

(44 5.0.7852 * loo = 8-52 percentile rank is 73 To indsssuch thed 2, OSina Z-table て20-32 coe-aet 5cote-45 48チ60 X,= 55-52 aod = 4.48 t 60 hoo scotes a 55-52 and 6448

75-60 ( Lt 14 = P(-0.36く < 1.07) Ko·8577-LI-O-6406 I 0.8577-0-3534