I need an explanation to all the questions. Need it completebefore 9 PM tomorrow.

- A z-score of z = +3.00 indicates a location that is ___.

- For a population with mean of 100 and standard deviation of 20, what is the X value corresponding to z=1.50?

-Juan took a Statistics exam and earned a 90%. If the exam scores are normally distributed with a mean = 75% and SD = 10%, what is Juan's z score?

-Based on Juan z-score, what percentage of student scored below Juan?

-Based on his z-score what percentage of student scored above Juan?

-What is the probability of randomly selecting a student who scored below Juan?

-What z-score roughly cut off the lower and upper 2.5% of the normal distribution? In other words, what two z-scores separate the middle 95% of the distribution from the tails?

- Lukas ran in a cross-country meet. He ran 3 miles in 23 minutes. Assume that the distribution of running times was normally distributed with a mean of 25 minutes and SD=1.5 minutes. What is the probability of randomly selecting a running time less than 23? In other words, what are the chances of randomly selecting a time that was faster than Lukas's? Round to two decimal places.

-Overall would you say that Lukas's time was relatively good, bad, or just average? Explain your answer.