Question

2. The random variable X denotes the average cost of out-of-state tuition with a mean of $25,600 and a variance of 1,000,000, i.e .X ∼ N ( 25 , 600 ; 1 , 000 , 000 ).   

If a random student is chosen in the US what is the probability their out of state tuition is greater than $24,100?

2B) What is the probability that a random out of state student has out-of-state tuition greater than 25,000 and less than 25,600? i.e.

2C) Suppose you randomly sample 50 students from the above distribution. What would the mean and variance of the sample mean's distribution be?

2D) What is the probability that the sample mean of the 50 students is less than 25,500? (round the intermediate z-score to the nearest second decimal)

2E) What is the probability the sample mean for out of state tuition is greater than $25,400 and less than 25,800, i.e P ( 25 , 400 < X < 25 , 800 ) (round the intermediate z-score to the nearest second decimal)

Answer 1