Homework SourseA A random variable X has a normal distribution with mean 25
A) A random variable X has a normal distribution with mean 2.5 and standard deviation 0.23. What is the 25th percentile of the distribution of X? Round your answer to two decimal places.
B)A random variable X has a normal distribution with mean 2.5 and standard deviation 0.23. What is the 80th percentile of the distribution of X? Round your answer to two decimal places.
C)A random variable X has a normal distribution with mean 2.5 and standard deviation 0.23. Calculate Pr{X < 1.9}. Round your answer to five decimal places.
D) A random variable X has a normal distribution with mean 2.5 and standard deviation 0.23. Calculate Pr{X > 3.4}. Round your answer to five decimal places.
E)A random variable X has a normal distribution with mean 2.5 and standard deviation 0.23. Calculate Pr{1.96 < X < 3.4}. Round your answer to five decimal places.
And how to solve these using R?
Solution
A
=NORM.INV(0.25,2.5,0.23)=2.34
B
=NORMINV(0.8,2.5,0.23)=2.69
C
=NORMDIST(1.9,2.5,0.23,FALSE)=0.05774
D
1-=NORMDIST(3.4,2.5,0.23,TRUE)=0.00005
