Answer to Question #115632 in Statistics and Probability for Wale

Question

Historically the results of a final exam given by a particular teacher have a mean of 65.3% with a standard deviation of 8.5.
Calculate the probability of a student getting a mark between
i) 75 and 85
ii) 79 and 81
iii) 79.9 and 80.1

Answer 1

1)P(75<X<85)=P(x<85)-P(x<75)

P(x<85); z=(x-μ)/σ=(85-65.3)/8.5=2.32, using table P(x<85)=0.98983

P(x<75); z=(75-65.3)/8.5=1.14, using table P(x<75)=0.87286

P(75<X<85)=0.98983-0.87286=0.117=11.7%

2)P(79<X<81)=P(x<81)-P(x<79)

P(x<81); z=(81-65.3)/8.5=1.85, using table P(x<81)=0.96784

P(x<79); z=(79-65.3)/8.5=1.61, using table P(x<79)=0.94630

P(79<X<81)=0.96784-0.94630=0.0215=2.15%

3)P(79.9<X<80.1)=P(x<80.1)-P(x<79.9)

P(x<80.1); z=(80.1-65.3)/8.5=1.74, using table P(x<80.1)=0.95907

P(x<79.9); z=(79.9-65.3)/8.5=1.72, using table P(x<79.9)=0.95728

P(79.9<X<80.1)=0.95907-0.95728=0.002=0.2%