Homework SourseA group of 1000 student wrote an entrance exam for the unive
A group of 1000 student wrote an entrance exam for the university of statistic.The mean is 62 and standard deviation of 12.assuming a normal distribution answer the following question A) how many people scored below 30. ( B) what is the probability of scoring between 60 and 80? Please show your steps.
A group of 1000 student wrote an entrance exam for the university of statistic.The mean is 62 and standard deviation of 12.assuming a normal distribution answer the following question A) how many people scored below 30. ( B) what is the probability of scoring between 60 and 80? Please show your steps.
Solution
Normal Distribution
Mean ( u ) =62
Standard Deviation ( sd )=12
Normal Distribution = Z= X- u / sd ~ N(0,1)
a)
P(X < 30) = (30-62)/12
= -32/12= -2.6667
= P ( Z <-2.6667) From Standard Normal Table
= 0.0038
b)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 60) = (60-62)/12
= -2/12 = -0.1667
= P ( Z <-0.1667) From Standard Normal Table
= 0.43382
P(X < 80) = (80-62)/12
= 18/12 = 1.5
= P ( Z <1.5) From Standard Normal Table
= 0.93319
P(60 < X < 80) = 0.93319-0.43382 = 0.4994
