Question

3. A normal distribution of BMCC MATSI scores has a standard deviation of 1.5. Find the z-scores corresponding to each of the following values: a. A score that is 3 points above the mean. b. A score that is 1.5 points below the mean. c. A score that is 2.25 points above the mean 4. Scores on BMCC fall 2017 MATI50.5 department final exam form a normal distribution with a mean of 70 and a standard deviation of 8. What percent of the population has the following? a. A score greater than 90 b. A score between 60 and 85 c. A score less than 60

Answer 1

2) Let μ denotes he mean score Given that standard deviahon we know that Z-scere i above he mean (u+ 3) Z -scove of a scone hat is 3 poinhs above the mean 1. 5 3 l: 5 below rhe mean is (n-1.5 The Scove otasc ore 5 points belo w the mean 군

abave he mean is (H 225) + 2.25 The 2-scove of a sco n e H、af- s 2 25 po oin above the mean 2 I. 5 2 25 - 15 4) Leh X denotes he scones. on 8Mcc falL 2017 MAT I50 5 depart ment final exam 2 we N70, 8 a〉 N ow pX - 70 , 90-70 - PZ 25

we kno w P 22 5) Φ.(z) is the cdf of ormal dishmibuHon standar d 0 9938 0 006 2 0 62 of the po pul ahon has a veaten han g0 b> P 60X85) 60 70 X-70 85 70 - P 125 875

(1.875)- 오(-1- 2 5 ) 史(1.875)_ {!- 重い25) (1.875) + φ(1.25) 0 96960 8944 -1 0 8640 a scove behween 60 and p x-7060-70 (-1,25 重(1.25丿 -0 8944 o 1056

of he populahon has Less han 60 a S 0 56